http://wiki.math.se/wikis/sf0600_0701/index.php?action=history&feed=atom&title=%C3%96vn_2.3 2026-04-24T21:09:13Z Versionshistorik för denna sida på wikin MediaWiki 1.9.3 http://wiki.math.se/wikis/sf0600_0701/index.php?title=%C3%96vn_2.3&diff=2237&oldid=prev 2007-07-16T07:59:33Z

<p>Tar bort sidans innehåll</p> <table border='0' width='98%' cellpadding='0' cellspacing='4' style="background-color: white;"> <tr> <td colspan='2' width='50%' align='center' style="background-color: white;">← Äldre version</td> <td colspan='2' width='50%' align='center' style="background-color: white;">Versionen från 16 juli 2007 kl. 07.59</td> </tr> <tr><td colspan="2" align="left"><strong>Rad 1:</strong></td> <td colspan="2" align="left"><strong>Rad 1:</strong></td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">__NOTOC__</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">==&amp;Ouml;vning 2.3:1==</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;div class=&quot;ovning&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">Kvadratkomplettera f&amp;ouml;ljande uttryck</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;25%&quot;&gt;$x^2-2x$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;25%&quot;&gt;$x^2+2x-1$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;25%&quot;&gt;$5+2x-x^2$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;d)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;25%&quot;&gt;$x^2+5x+3$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/table&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/div&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">==&amp;Ouml;vning 2.3:2==</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;div class=&quot;ovning&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">L&amp;ouml;s f&amp;ouml;ljande andragradsekvationer med kvadratkomplettering</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$x^2-4x+3=0$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$y^2+2y-15=0$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$y^2+3y+4=0$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;d)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$4x^2-28x+13=0$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;e)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$5x^2+2x-3=0$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;f)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$3x^2-10x+8=0$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/table&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/div&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;"></td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">==&amp;Ouml;vning 2.3:3==</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;div class=&quot;ovning&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">L&amp;ouml;s f&amp;ouml;ljande ekvationer direkt</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$x(x+3)=0$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$(x-3)(x+5)=0$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$5(3x-2)(x+8)=0$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;d)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$x(x+3)-x(2x-9)=0$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;e)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$(x+3)(x-1)-(x+3)(2x-9)=0$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;f)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$x(x^2-2x)+x(2-x)=0$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/table&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/div&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;"></td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">==&amp;Ouml;vning 2.3:4==</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;div class=&quot;ovning&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">Best&amp;auml;m en andragradsekvation som har r&amp;ouml;tterna</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;100%&quot;&gt;$-1\ $ och $\ 2$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;100%&quot;&gt;$1+\sqrt{3}\ $ och $\ 1-\sqrt{3}$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;100%&quot;&gt;$3\ $ och $\ \sqrt{3}$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/table&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/div&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;"></td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">==&amp;Ouml;vning 2.3:5==</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;div class=&quot;ovning&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;100%&quot;&gt;Best&amp;auml;m en andragradsekvation som bara har $\,-7\,$ som rot.&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr&gt; </td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;100%&quot;&gt;Best&amp;auml;m ett v&amp;auml;rde p&amp;aring; $\,x\,$ som g&amp;ouml;r att uttrycket $\,4x^2-28x+48\,$ &amp;auml;r negativt.&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;100%&quot;&gt;Ekvationen $\,x^2+4x+b=0\,$ har en rot $\,x=1\,$. Best&amp;auml;m v&amp;auml;rdet p&amp;aring; konstanten $\,b\,$.&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/table&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/div&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;"></td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">==&amp;Ouml;vning 2.3:6==</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;div class=&quot;ovning&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">Best&amp;auml;m det minsta v&amp;auml;rde som f&amp;ouml;ljande polynom antar</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$x^2-2x+1$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$x^2-4x+2$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$x^2-5x+7$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/table&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/div&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;"></td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">==&amp;Ouml;vning 2.3:7==</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;div class=&quot;ovning&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">Best&amp;auml;m det st&amp;ouml;rsta v&amp;auml;rde som f&amp;ouml;ljande polynom antar</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$1-x^2$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$-x^2+3x-4$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$x^2+x+1$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/table&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/div&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;"></td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">==&amp;Ouml;vning 2.3:8==</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;div class=&quot;ovning&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">Skissera grafen till f&amp;ouml;ljande funktioner</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$f(x)=x^2+1$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$f(x)=(x-1)^2+2$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$f(x)=x^2-6x+11$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/table&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/div&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;"></td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">==&amp;Ouml;vning 2.3:9==</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;div class=&quot;ovning&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">Hitta alla sk&amp;auml;rningspunkter mellan x-axeln och kurvan</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$y=x^2-1$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$y=x^2-5x+6$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$y=3x^2-12x+9$&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/table&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/div&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;"></td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">==&amp;Ouml;vning 2.3:10==</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;div class=&quot;ovning&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">Rita in i ett ''xy''-plan alla punkter vars koordinater $\,(x,y)\,$ uppfyller</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$y \geq x^2\ $ och $\ y \leq 1 $&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$y \leq 1-x^2\ $ och $\ x \geq 2y-3 $&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$1 \geq x \geq y^2 $&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;d)&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$x^2 \leq y \leq x $&lt;/td&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/table&gt;</td><td colspan="2">&nbsp;</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;">&lt;/div&gt;</td><td colspan="2">&nbsp;</td></tr> </table>

KTH.SE:u1zpa8nw http://wiki.math.se/wikis/sf0600_0701/index.php?title=%C3%96vn_2.3&diff=2235&oldid=prev 2007-07-16T07:57:44Z

<p></p> <table border='0' width='98%' cellpadding='0' cellspacing='4' style="background-color: white;"> <tr> <td colspan='2' width='50%' align='center' style="background-color: white;">← Äldre version</td> <td colspan='2' width='50%' align='center' style="background-color: white;">Versionen från 16 juli 2007 kl. 07.57</td> </tr> <tr><td colspan="2" align="left"><strong>Rad 1:</strong></td> <td colspan="2" align="left"><strong>Rad 1:</strong></td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;">__NOTOC__</td><td> </td><td style="background: #eee; font-size: smaller;">__NOTOC__</td></tr> <tr><td>-</td><td style="background: #ffa; font-size: smaller;"></td><td colspan="2">&nbsp;</td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;">==&amp;Ouml;vning 2.3:1==</td><td> </td><td style="background: #eee; font-size: smaller;">==&amp;Ouml;vning 2.3:1==</td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;">&lt;div class=&quot;ovning&quot;&gt;</td><td> </td><td style="background: #eee; font-size: smaller;">&lt;div class=&quot;ovning&quot;&gt;</td></tr> </table>

KTH.SE:u1zpa8nw http://wiki.math.se/wikis/sf0600_0701/index.php?title=%C3%96vn_2.3&diff=2234&oldid=prev 2007-07-16T07:57:39Z

<p></p> <table border='0' width='98%' cellpadding='0' cellspacing='4' style="background-color: white;"> <tr> <td colspan='2' width='50%' align='center' style="background-color: white;">← Äldre version</td> <td colspan='2' width='50%' align='center' style="background-color: white;">Versionen från 16 juli 2007 kl. 07.57</td> </tr> <tr><td colspan="2" align="left"><strong>Rad 1:</strong></td> <td colspan="2" align="left"><strong>Rad 1:</strong></td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">__NOTOC__</td></tr> <tr><td> </td><td style="background: #eee; font-size: smaller;"></td><td> </td><td style="background: #eee; font-size: smaller;"></td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">==&amp;Ouml;vning 2.3:1==</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;div class=&quot;ovning&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">Kvadratkomplettera f&amp;ouml;ljande uttryck</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;25%&quot;&gt;$x^2-2x$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;25%&quot;&gt;$x^2+2x-1$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;25%&quot;&gt;$5+2x-x^2$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;d)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;25%&quot;&gt;$x^2+5x+3$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/table&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/div&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;"></td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">==&amp;Ouml;vning 2.3:2==</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;div class=&quot;ovning&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">L&amp;ouml;s f&amp;ouml;ljande andragradsekvationer med kvadratkomplettering</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$x^2-4x+3=0$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$y^2+2y-15=0$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$y^2+3y+4=0$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;d)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$4x^2-28x+13=0$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;e)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$5x^2+2x-3=0$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;f)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$3x^2-10x+8=0$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/table&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/div&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;"></td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">==&amp;Ouml;vning 2.3:3==</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;div class=&quot;ovning&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">L&amp;ouml;s f&amp;ouml;ljande ekvationer direkt</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$x(x+3)=0$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$(x-3)(x+5)=0$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$5(3x-2)(x+8)=0$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;d)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$x(x+3)-x(2x-9)=0$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;e)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$(x+3)(x-1)-(x+3)(2x-9)=0$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;f)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$x(x^2-2x)+x(2-x)=0$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/table&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/div&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;"></td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">==&amp;Ouml;vning 2.3:4==</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;div class=&quot;ovning&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">Best&amp;auml;m en andragradsekvation som har r&amp;ouml;tterna</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;100%&quot;&gt;$-1\ $ och $\ 2$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;100%&quot;&gt;$1+\sqrt{3}\ $ och $\ 1-\sqrt{3}$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;100%&quot;&gt;$3\ $ och $\ \sqrt{3}$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/table&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/div&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;"></td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">==&amp;Ouml;vning 2.3:5==</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;div class=&quot;ovning&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;100%&quot;&gt;Best&amp;auml;m en andragradsekvation som bara har $\,-7\,$ som rot.&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr&gt; </td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;100%&quot;&gt;Best&amp;auml;m ett v&amp;auml;rde p&amp;aring; $\,x\,$ som g&amp;ouml;r att uttrycket $\,4x^2-28x+48\,$ &amp;auml;r negativt.&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;100%&quot;&gt;Ekvationen $\,x^2+4x+b=0\,$ har en rot $\,x=1\,$. Best&amp;auml;m v&amp;auml;rdet p&amp;aring; konstanten $\,b\,$.&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/table&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/div&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;"></td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">==&amp;Ouml;vning 2.3:6==</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;div class=&quot;ovning&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">Best&amp;auml;m det minsta v&amp;auml;rde som f&amp;ouml;ljande polynom antar</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$x^2-2x+1$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$x^2-4x+2$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$x^2-5x+7$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/table&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/div&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;"></td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">==&amp;Ouml;vning 2.3:7==</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;div class=&quot;ovning&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">Best&amp;auml;m det st&amp;ouml;rsta v&amp;auml;rde som f&amp;ouml;ljande polynom antar</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$1-x^2$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$-x^2+3x-4$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$x^2+x+1$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/table&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/div&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;"></td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">==&amp;Ouml;vning 2.3:8==</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;div class=&quot;ovning&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">Skissera grafen till f&amp;ouml;ljande funktioner</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$f(x)=x^2+1$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$f(x)=(x-1)^2+2$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$f(x)=x^2-6x+11$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/table&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/div&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;"></td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">==&amp;Ouml;vning 2.3:9==</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;div class=&quot;ovning&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">Hitta alla sk&amp;auml;rningspunkter mellan x-axeln och kurvan</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$y=x^2-1$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$y=x^2-5x+6$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$y=3x^2-12x+9$&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/table&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/div&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;"></td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">==&amp;Ouml;vning 2.3:10==</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;div class=&quot;ovning&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">Rita in i ett ''xy''-plan alla punkter vars koordinater $\,(x,y)\,$ uppfyller</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$y \geq x^2\ $ och $\ y \leq 1 $&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$y \leq 1-x^2\ $ och $\ x \geq 2y-3 $&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr align=&quot;left&quot;&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$1 \geq x \geq y^2 $&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot;&gt;d)&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$x^2 \leq y \leq x $&lt;/td&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/table&gt;</td></tr> <tr><td colspan="2">&nbsp;</td><td>+</td><td style="background: #cfc; font-size: smaller;">&lt;/div&gt;</td></tr> </table>

KTH.SE:u1zpa8nw http://wiki.math.se/wikis/sf0600_0701/index.php?title=%C3%96vn_2.3&diff=2131&oldid=prev 2007-06-21T15:08:17Z

<p>Tar bort sidans innehåll</p> <a href="http://wiki.math.se/wikis/sf0600_0701/index.php?title=%C3%96vn_2.3&amp;diff=2131&amp;oldid=2128">(Skillnad mellan versioner)</a>

KTH.SE:u1xsetv1 http://wiki.math.se/wikis/sf0600_0701/index.php?title=%C3%96vn_2.3&diff=2128&oldid=prev 2007-06-21T14:56:26Z

<p>Ny sida: ==&amp;Ouml;vning 2.3:1== &lt;div class=&quot;ovning&quot;&gt; Kvadratkomplettera f&amp;ouml;ljande uttryck &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt; &lt;tr align=&quot;left&quot;&gt; &lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt; &lt;td class=&quot;ntext&quot; wi...</p> <p><b>Ny sida</b></p><div>==&amp;Ouml;vning 2.3:1==<br /> <br /> &lt;div class=&quot;ovning&quot;&gt;<br /> Kvadratkomplettera f&amp;ouml;ljande uttryck<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;25%&quot;&gt;$x^2-2x$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;25%&quot;&gt;$x^2+2x-1$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;25%&quot;&gt;$5+2x-x^2$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;d)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;25%&quot;&gt;$x^2+5x+3$&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=&quot;svar&quot;&gt;<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;25%&quot;&gt;$(x-1)^2-1$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;25%&quot;&gt;$(x+1)^2-2$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;25%&quot;&gt;$-(x-1)^2+6$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;d)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;25%&quot;&gt;$\bigl(x+\frac{5}{2}\bigr)^2-\frac{13}{4}$&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning a)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga a)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_1a.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning b)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga b)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_1b.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning c)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga c)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_1c.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning d)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga d)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_1d.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> ==&amp;Ouml;vning 2.3:2==<br /> <br /> &lt;div class=&quot;ovning&quot;&gt;<br /> L&amp;ouml;s f&amp;ouml;ljande andragradsekvationer med kvadratkomplettering<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$x^2-4x+3=0$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$y^2+2y-15=0$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$y^2+3y+4=0$&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;d)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$4x^2-28x+13=0$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;e)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$5x^2+2x-3=0$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;f)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$3x^2-10x+8=0$&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;Facit&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Facit till alla delfrågor&lt;br \&gt;<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$\left\{ \eqalign{ x_1 &amp;= 1 \cr x_2 &amp;= 3\cr }\right.$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$\left\{ \eqalign{ y_1 &amp;= -5 \cr y_2 &amp;= 3\cr }\right.$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt; saknar (reella) l&amp;ouml;sning&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;d)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$ \left\{ \eqalign{ x_1 &amp;= \textstyle\frac{1}{2}\cr x_2 &amp;= \textstyle\frac{13}{2}\cr }\right.$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;e)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$\left\{ \eqalign{ x_1 &amp;= -1 \cr x_2 &amp;= \textstyle\frac{3}{5}\cr }\right.$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;f)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$ \left\{ \eqalign{ x_1 &amp;= \textstyle\frac{4}{3}\cr x_2 &amp;= 2\cr }\right.$&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning a)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga a)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_2a.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;/div&gt;<br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning b)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga b)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_2b.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;/div&gt;<br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning c)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga c)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_2c.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning d)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga d)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_2d.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning e)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga e)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_2e.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning f)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga f)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_2f.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> ==&amp;Ouml;vning 2.3:3==<br /> <br /> &lt;div class=&quot;ovning&quot;&gt;<br /> L&amp;ouml;s f&amp;ouml;ljande ekvationer direkt<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$x(x+3)=0$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$(x-3)(x+5)=0$&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$5(3x-2)(x+8)=0$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;d)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$x(x+3)-x(2x-9)=0$&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;e)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$(x+3)(x-1)-(x+3)(2x-9)=0$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;f)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$x(x^2-2x)+x(2-x)=0$&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;Facit&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Facit till alla delfrågor&lt;br \&gt;<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$\left\{ \eqalign{ x_1 &amp;= 0 \cr x_2 &amp; = -3\cr }\right.$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$\left\{ \eqalign{ x_1 &amp;= 3 \cr x_2 &amp; = -5\cr }\right. $&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$\left\{ \eqalign{ x_1 &amp; = \textstyle\frac{2}{3} \cr x_2 &amp; = -8\cr }\right. $&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;d)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$\left\{ \eqalign{ x_1 &amp; = 0\cr x_2 &amp; = 12\cr }\right. $&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;e)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$\left\{ \eqalign{ x_1 &amp; = -3 \cr x_2 &amp; = 8\cr }\right. $&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;f)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$\left\{ \eqalign{ x_1 &amp; = 0 \cr x_2 &amp; = 1 \cr x_3 &amp; = 2 }\right. $&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning a)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga a)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_3a.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning b)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga b)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_3b.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning c)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga c)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_3c.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning d)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga d)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_3d.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning e)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga e)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_3e.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning f)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga f)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_3f.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> ==&amp;Ouml;vning 2.3:4==<br /> <br /> &lt;div class=&quot;ovning&quot;&gt;<br /> Best&amp;auml;m en andragradsekvation som har r&amp;ouml;tterna<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;100%&quot;&gt;$-1\ $ och $\ 2$&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;100%&quot;&gt;$1+\sqrt{3}\ $ och $\ 1-\sqrt{3}$&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;100%&quot;&gt;$3\ $ och $\ \sqrt{3}$&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;Facit&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Facit till alla delfrågor<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;100%&quot;&gt;$ax^2-ax-2a=0\,$, där $\,a\ne 0\,$ är en konstant.&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr align=&quot;left&quot;&gt; <br /> &lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;100%&quot;&gt;$ax^2-2ax-2a=0\,$, där $\,a\ne 0\,$ är en konstant.&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;100%&quot;&gt;$ax^2-(3+\sqrt{3}\,)ax+3\sqrt{3}\,a=0\,$, där $\,a\ne 0\,$ är en konstant.&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning a)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga a)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_4a-1(2).gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_4a-2(2).gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning b)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga b)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_4b-1(2).gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_4b-2(2).gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning c)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga c)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_4c.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> ==&amp;Ouml;vning 2.3:5==<br /> <br /> &lt;div class=&quot;ovning&quot;&gt;<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;100%&quot;&gt;Best&amp;auml;m en andragradsekvation som bara har $\,-7\,$ som rot.&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr&gt; <br /> &lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;100%&quot;&gt;Best&amp;auml;m ett v&amp;auml;rde p&amp;aring; $\,x\,$ som g&amp;ouml;r att uttrycket $\,4x^2-28x+48\,$ &amp;auml;r negativt.&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;100%&quot;&gt;Ekvationen $\,x^2+4x+b=0\,$ har en rot $\,x=1\,$. Best&amp;auml;m v&amp;auml;rdet p&amp;aring; konstanten $\,b\,$.&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;Facit&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Facit till alla delfrågor<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;100%&quot;&gt;Exempelvis $\ x^2+14x+49=0\,$.&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;100%&quot;&gt;$3&lt; x&lt;4$&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;100%&quot;&gt;$b=-5$&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning a&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga a)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_5a.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning b)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga b)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_5b.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning c)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga c)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_5c.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> ==&amp;Ouml;vning 2.3:6==<br /> <br /> &lt;div class=&quot;ovning&quot;&gt;<br /> Best&amp;auml;m det minsta v&amp;auml;rde som f&amp;ouml;ljande polynom antar<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$x^2-2x+1$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$x^2-4x+2$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$x^2-5x+7$&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;<br /> &lt;/table&gt;<br /> <br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;Facit&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Facit till alla delfrågor<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$0$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$-2$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$\displaystyle \frac{3}{4}$&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning a)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga a)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_6a.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning b)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga b)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_6b.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning c)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga c)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_6c.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> ==&amp;Ouml;vning 2.3:7==<br /> <br /> &lt;div class=&quot;ovning&quot;&gt;<br /> Best&amp;auml;m det st&amp;ouml;rsta v&amp;auml;rde som f&amp;ouml;ljande polynom antar<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$1-x^2$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$-x^2+3x-4$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$x^2+x+1$&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;Facit&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Facit till alla delfrågor&lt;br \&gt;<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$1$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$\displaystyle -\frac{7}{4}$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;saknar max&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning a)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga a)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_7a.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning b)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga b)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_7b.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning c)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga c)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_7c.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> ==&amp;Ouml;vning 2.3:8==<br /> <br /> &lt;div class=&quot;ovning&quot;&gt;<br /> Skissera grafen till f&amp;ouml;ljande funktioner<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$f(x)=x^2+1$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$f(x)=(x-1)^2+2$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$f(x)=x^2-6x+11$&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;Facit&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Facit till alla delfrågor&lt;br \&gt;<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td&gt;Se lösningarna.&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning a)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga a)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_8a.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning b)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga b)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_8b.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;L&amp;ouml;sning c)&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Lösning till delfråga c)<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr&gt;<br /> &lt;td align=&quot;center&quot;&gt;<br /> [[Bild:2_3_8c.gif]]<br /> &lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> ==&amp;Ouml;vning 2.3:9==<br /> <br /> &lt;div class=&quot;ovning&quot;&gt;<br /> Hitta alla sk&amp;auml;rningspunkter mellan x-axeln och kurvan<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$y=x^2-1$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$y=x^2-5x+6$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$y=3x^2-12x+9$&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;Facit&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Facit till alla delfrågor<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$(-1,0)\ $ och $\ (1,0)$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$(2,0)\ $ och $\ (3,0)$&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;33%&quot;&gt;$(1,0)\ $ och $\ (3,0)$&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;<br /> <br /> <br /> <br /> ==&amp;Ouml;vning 2.3:10==<br /> <br /> &lt;div class=&quot;ovning&quot;&gt;<br /> Rita in i ett ''xy''-plan alla punkter vars koordinater $\,(x,y)\,$ uppfyller<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;a)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$y \geq x^2\ $ och $\ y \leq 1 $&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;b)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$y \leq 1-x^2\ $ och $\ x \geq 2y-3 $&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;c)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$1 \geq x \geq y^2 $&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot;&gt;d)&lt;/td&gt;<br /> &lt;td class=&quot;ntext&quot; width=&quot;50%&quot;&gt;$x^2 \leq y \leq x $&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;tr&gt;&lt;td height=&quot;5px&quot;/&gt;&lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> <br /> &lt;div class=NavFrame style=&quot;CLEAR: both&quot;&gt;<br /> &lt;div class=NavHead&gt;Facit&amp;nbsp;&lt;/div&gt;<br /> &lt;div class=NavContent&gt;<br /> Facit till alla delfrågor<br /> &lt;table width=&quot;100%&quot; cellspacing=&quot;10px&quot;&gt;<br /> &lt;tr align=&quot;left&quot;&gt;<br /> &lt;td&gt;Se lösningarna.&lt;/td&gt;<br /> &lt;/tr&gt;<br /> &lt;/table&gt;<br /> &lt;/div&gt;<br /> &lt;/div&gt;</div>

KTH.SE:u1xsetv1