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> |