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Övningar 2.3 - Versionshistorik
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KTH.SE:u1zpa8nw: Ny sida: __NOTOC__ ==Övning 2.3:1== <div class="ovning"> Kvadratkomplettera följande uttryck <table width="100%" cellspacing="10px"> <tr align="left"> <td class="ntext">a)</td> <td class="...
2007-07-16T07:58:56Z
<p>Ny sida: __NOTOC__ ==&Ouml;vning 2.3:1== <div class="ovning"> Kvadratkomplettera f&ouml;ljande uttryck <table width="100%" cellspacing="10px"> <tr align="left"> <td class="ntext">a)</td> <td class="...</p>
<p><b>Ny sida</b></p><div>__NOTOC__<br />
==&Ouml;vning 2.3:1==<br />
<div class="ovning"><br />
Kvadratkomplettera f&ouml;ljande uttryck<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="25%">$x^2-2x$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="25%">$x^2+2x-1$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="25%">$5+2x-x^2$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="25%">$x^2+5x+3$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 2.3:2==<br />
<div class="ovning"><br />
L&ouml;s f&ouml;ljande andragradsekvationer med kvadratkomplettering<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$x^2-4x+3=0$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$y^2+2y-15=0$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$y^2+3y+4=0$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="33%">$4x^2-28x+13=0$</td><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="33%">$5x^2+2x-3=0$</td><br />
<td class="ntext">f)</td><br />
<td class="ntext" width="33%">$3x^2-10x+8=0$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 2.3:3==<br />
<div class="ovning"><br />
L&ouml;s f&ouml;ljande ekvationer direkt<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$x(x+3)=0$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$(x-3)(x+5)=0$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$5(3x-2)(x+8)=0$</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="50%">$x(x+3)-x(2x-9)=0$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">e)</td><br />
<td class="ntext" width="50%">$(x+3)(x-1)-(x+3)(2x-9)=0$</td><br />
<td class="ntext">f)</td><br />
<td class="ntext" width="50%">$x(x^2-2x)+x(2-x)=0$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 2.3:4==<br />
<div class="ovning"><br />
Best&auml;m en andragradsekvation som har r&ouml;tterna<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="100%">$-1\ $ och $\ 2$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="100%">$1+\sqrt{3}\ $ och $\ 1-\sqrt{3}$</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="100%">$3\ $ och $\ \sqrt{3}$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 2.3:5==<br />
<div class="ovning"><br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="100%">Best&auml;m en andragradsekvation som bara har $\,-7\,$ som rot.</td><br />
</tr><br />
<tr> <br />
<td class="ntext">b)</td><br />
<td class="ntext" width="100%">Best&auml;m ett v&auml;rde p&aring; $\,x\,$ som g&ouml;r att uttrycket $\,4x^2-28x+48\,$ &auml;r negativt.</td><br />
</tr><br />
<tr><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="100%">Ekvationen $\,x^2+4x+b=0\,$ har en rot $\,x=1\,$. Best&auml;m v&auml;rdet p&aring; konstanten $\,b\,$.</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 2.3:6==<br />
<div class="ovning"><br />
Best&auml;m det minsta v&auml;rde som f&ouml;ljande polynom antar<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$x^2-2x+1$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$x^2-4x+2$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$x^2-5x+7$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 2.3:7==<br />
<div class="ovning"><br />
Best&auml;m det st&ouml;rsta v&auml;rde som f&ouml;ljande polynom antar<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$1-x^2$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$-x^2+3x-4$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$x^2+x+1$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 2.3:8==<br />
<div class="ovning"><br />
Skissera grafen till f&ouml;ljande funktioner<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$f(x)=x^2+1$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$f(x)=(x-1)^2+2$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$f(x)=x^2-6x+11$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 2.3:9==<br />
<div class="ovning"><br />
Hitta alla sk&auml;rningspunkter mellan x-axeln och kurvan<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="33%">$y=x^2-1$</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="33%">$y=x^2-5x+6$</td><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="33%">$y=3x^2-12x+9$</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div><br />
<br />
==&Ouml;vning 2.3:10==<br />
<div class="ovning"><br />
Rita in i ett ''xy''-plan alla punkter vars koordinater $\,(x,y)\,$ uppfyller<br />
<table width="100%" cellspacing="10px"><br />
<tr align="left"><br />
<td class="ntext">a)</td><br />
<td class="ntext" width="50%">$y \geq x^2\ $ och $\ y \leq 1 $</td><br />
<td class="ntext">b)</td><br />
<td class="ntext" width="50%">$y \leq 1-x^2\ $ och $\ x \geq 2y-3 $</td><br />
</tr><br />
<tr align="left"><br />
<td class="ntext">c)</td><br />
<td class="ntext" width="50%">$1 \geq x \geq y^2 $</td><br />
<td class="ntext">d)</td><br />
<td class="ntext" width="50%">$x^2 \leq y \leq x $</td><br />
</tr><br />
<tr><td height="5px"/></tr><br />
</table><br />
</div></div>
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