Övn 2.3
Sommarmatte 1
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| - | __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="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> | ||
| - | |||
| - | ==Övning 2.3:2== | ||
| - | <div class="ovning"> | ||
| - | Lös följande 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> | ||
| - | |||
| - | ==Övning 2.3:3== | ||
| - | <div class="ovning"> | ||
| - | Lös följande 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> | ||
| - | |||
| - | ==Övning 2.3:4== | ||
| - | <div class="ovning"> | ||
| - | Bestäm en andragradsekvation som har rötterna | ||
| - | <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> | ||
| - | |||
| - | ==Övning 2.3:5== | ||
| - | <div class="ovning"> | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="100%">Bestäm en andragradsekvation som bara har $\,-7\,$ som rot.</td> | ||
| - | </tr> | ||
| - | <tr> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="100%">Bestäm ett värde på $\,x\,$ som gör att uttrycket $\,4x^2-28x+48\,$ är negativt.</td> | ||
| - | </tr> | ||
| - | <tr> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="100%">Ekvationen $\,x^2+4x+b=0\,$ har en rot $\,x=1\,$. Bestäm värdet på konstanten $\,b\,$.</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | ==Övning 2.3:6== | ||
| - | <div class="ovning"> | ||
| - | Bestäm det minsta värde som följande 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> | ||
| - | |||
| - | ==Övning 2.3:7== | ||
| - | <div class="ovning"> | ||
| - | Bestäm det största värde som följande 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> | ||
| - | |||
| - | ==Övning 2.3:8== | ||
| - | <div class="ovning"> | ||
| - | Skissera grafen till följande 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> | ||
| - | |||
| - | ==Övning 2.3:9== | ||
| - | <div class="ovning"> | ||
| - | Hitta alla skärningspunkter 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> | ||
| - | |||
| - | ==Övning 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> | ||
