Rev 16458 | Details | Compare with Previous | Last modification | View Log | RSS feed
| Rev | Author | Line No. | Line |
|---|---|---|---|
| 16458 | bpr | 1 | |
| 2 | \def{text tab1=slib(function/tabsignes [[x,-Inf,,+Inf;f(x),,+,]])} |
||
| 3 | \def{text tab2=slib(function/tabsignes [[x,-Inf,,x_S,,+Inf;f(x),,+,0,+]])} |
||
| 4 | \def{text tab3=slib(function/tabsignes [[x,-Inf,,x_1,,x_2,,+Inf;f(x),,+,0,-,0,+]])} |
||
| 5 | \def{text tab4=slib(function/tabsignes [[x,-Inf,,+Inf;f(x),,-,]])} |
||
| 6 | \def{text tab5=slib(function/tabsignes [[x,-Inf,,x_S,,+Inf;f(x),,-,0,-]])} |
||
| 7 | \def{text tab6=slib(function/tabsignes [[x,-Inf,,x_2,,x_1,,+Inf;f(x),,-,0,+,0,-]])} |
||
| 8 | <p>Trinôme \(f(x)=a*x^2+b*x+c) avec \(a \ne 0), |
||
| 9 | \(\Delta=b^2-4 a c), |
||
| 16297 | bpr | 10 | \(f(x) = a (x - x_S)^2 + y_S) avec \(x_S=\frac{-b}{2a}) et \(y_S=f(x_S))</p> |
| 16458 | bpr | 11 | <table class="wimscenter"> |
| 12 | <tr><td></td><td>\(\Delta \lt 0)</td> |
||
| 13 | <td>\(\Delta = 0)</td><td>\(\Delta \gt 0)</td></tr> |
||
| 16297 | bpr | 14 | <tr><td>\(a \gt 0)</td> |
| 16458 | bpr | 15 | <td>\draw{200,200}{ |
| 16297 | bpr | 16 | xrange -2,8 |
| 17 | yrange -2,8 |
||
| 18 | arrow -2,0,8,0,8, black |
||
| 19 | arrow 0,-2,0,8,8, black |
||
| 20 | dline 0,1,3,1,red |
||
| 21 | dline 3,0,3,1,red |
||
| 16458 | bpr | 22 | text red,2.9,-0.1 , large, x |
| 23 | text red,3.4,-0.5, small, S |
||
| 24 | text red,-1,1.5, large,y |
||
| 25 | text red,-0.5,1, small, S |
||
| 26 | plot black,(x-3)^2+1 |
||
| 27 | text black,1.7,4.5, large, f |
||
| 16297 | bpr | 28 | } |
| 17280 | bpr | 29 | <br>cas 1<br> \tab1 |
| 16458 | bpr | 30 | </td><td> |
| 16297 | bpr | 31 | \draw{200,200}{ |
| 32 | xrange -2,8 |
||
| 33 | yrange -2,8 |
||
| 34 | arrow -2,0,8,0,8, black |
||
| 16458 | bpr | 35 | text red,2.9,-0.1,large,x |
| 36 | text red,3.4,-0.5,small,S |
||
| 16297 | bpr | 37 | plot black, (x-3)^2 |
| 16458 | bpr | 38 | text black1.7,4.5, large, f |
| 16297 | bpr | 39 | } |
| 17280 | bpr | 40 | <br>cas 2<br>\tab2 |
| 16458 | bpr | 41 | </td><td> |
| 16297 | bpr | 42 | \draw{200,200}{ |
| 43 | xrange -2,8 |
||
| 44 | yrange -5,5 |
||
| 45 | arrow -2,0,8,0,8, black |
||
| 46 | arrow 0,-5,0,5,8, black |
||
| 47 | dline 0,-2,3,-2,red |
||
| 48 | dline 3,0,3,-2,red |
||
| 16458 | bpr | 49 | text red,2.9,1,large, x |
| 50 | text red,3.4,0.6,small, S |
||
| 51 | text red,1.1,-0.1,large, x |
||
| 52 | text red,1.6,-0.6,small, 1 |
||
| 53 | text red,4.5,-0.1,large, x |
||
| 54 | text red,5,-0.6,small, 2 |
||
| 55 | text red,-1,-1.5,large,y |
||
| 56 | text red,-0.5,-2,small, S |
||
| 16297 | bpr | 57 | plot black, (x-3)^2-2 |
| 16458 | bpr | 58 | text black,1.7,1.5,large, f |
| 16297 | bpr | 59 | } |
| 17280 | bpr | 60 | <br>cas 3<br>\tab3 |
| 16458 | bpr | 61 | </td></tr> |
| 62 | <tr><td>\(a \lt 0)</td><td> |
||
| 16297 | bpr | 63 | \draw{200,200}{ |
| 64 | xrange -2,8 |
||
| 65 | yrange -8,2 |
||
| 66 | arrow -2,0,8,0,8, black |
||
| 67 | arrow 0,-8,0,2,8, black |
||
| 68 | dline 0,-1,3,-1,red |
||
| 69 | dline 3,0,3,-1,red |
||
| 70 | text red, 2.9,1 , large, x |
||
| 71 | text red, 3.4,0.6, small, S |
||
| 72 | text red, -1,-0.5, large,y |
||
| 73 | text red, -0.5,-1, small, S |
||
| 74 | plot black, -(x-3)^2-1 |
||
| 75 | text black, 1.7,-4.5, large, f |
||
| 17280 | bpr | 76 | }<br>\tab4<br>cas 4 |
| 16458 | bpr | 77 | </td><td> |
| 16297 | bpr | 78 | \draw{200,200}{ |
| 79 | xrange -2,8 |
||
| 80 | yrange -8,2 |
||
| 81 | arrow -2,0,8,0,8, black |
||
| 82 | text red, 2.9,1 , large, x |
||
| 83 | text red, 3.4,0.6, small, S |
||
| 84 | plot black, -(x-3)^2 |
||
| 85 | text black, 1.7,-4.5, large, f |
||
| 86 | } |
||
| 17280 | bpr | 87 | <br>\tab5<br>cas 5 |
| 16458 | bpr | 88 | </td><td> |
| 16297 | bpr | 89 | \draw{200,200}{ |
| 90 | xrange -2,8 |
||
| 91 | yrange -5,5 |
||
| 92 | arrow -2,0,8,0,8, black |
||
| 93 | arrow 0,-5,0,5,8, black |
||
| 94 | dline 0,2,3,2,red |
||
| 95 | dline 3,0,3,2,red |
||
| 96 | text red, 2.9,-0.1, large, x |
||
| 97 | text red, 3.4,-0.6, small, S |
||
| 98 | text red, 1.6,-0.1 , large, x |
||
| 99 | text red, 2.1,-0.6, small, 2 |
||
| 100 | text red, 4,-0.1 , large, x |
||
| 101 | text red, 4.5,-0.6, small, 1 |
||
| 102 | text red, -1,2.5, large,y |
||
| 103 | text red, -0.5,2, small, S |
||
| 104 | plot black, -(x-3)^2+2 |
||
| 105 | text black, 1.7,-1.5, large, f |
||
| 106 | } |
||
| 17280 | bpr | 107 | <br>\tab6<br>cas 6 |
| 16458 | bpr | 108 | </td> |
| 16297 | bpr | 109 | </tr> |
| 110 | <tr><td>Racines<br>Solutions de<br>\(f(x) = 0)</td><td>Pas de racine.</td><td>\(x_S = x_1 = x_2 = \frac{-b}{2 a})</td><td>\(x_1=\frac{-b-\sqrt{\Delta}}{2 a}) et \(x_2=\frac{-b+\sqrt{\Delta}}{2 a})</td></tr> |
||
| 111 | <tr><td>Factorisation</td><td>Pas de factorisation</td><td>\(f(x) = a (x - x_S)^2)</td><td>\(f(x) = a (x - x_1) (x - x_2))</td></tr> |
||
| 112 | </table> |