Övn 2.3

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

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