!set titb=Allure de la courbe et formules du trinôme
!set keyw=
!set datm=20210824
!set prev=
!set next=
!set upbl=main
!set dat1=19000101
!set dat2=24000101

!if $wims_read_parm!=$empty
  !goto $wims_read_parm
!endif
!exit

:content


!readproc slib/function/tabsignes [[x,-Inf,,+Inf;f(x),,+,]] 
!set tmp0=$slib_out
!set m_tab1=$(tmp0)

!readproc slib/function/tabsignes [[x,-Inf,,x_S,,+Inf;f(x),,+,0,+]] 
!set tmp0=$slib_out
!set m_tab2=$(tmp0)

!readproc slib/function/tabsignes [[x,-Inf,,x_1,,x_2,,+Inf;f(x),,+,0,-,0,+]] 
!set tmp0=$slib_out
!set m_tab3=$(tmp0)

!readproc slib/function/tabsignes [[x,-Inf,,+Inf;f(x),,-,]] 
!set tmp0=$slib_out
!set m_tab4=$(tmp0)

!readproc slib/function/tabsignes [[x,-Inf,,x_S,,+Inf;f(x),,-,0,-]] 
!set tmp0=$slib_out
!set m_tab5=$(tmp0)

!readproc slib/function/tabsignes [[x,-Inf,,x_2,,x_1,,+Inf;f(x),,-,0,+,0,-]] 
!set tmp0=$slib_out
!set m_tab6=$(tmp0)

<p>Trinôme 
!insmath f(x)=a*x^2+b*x+c
 avec 
!insmath a \ne 0
,

!insmath \Delta=b^2-4 a c
,

!insmath f(x) = a (x - x_S)^2 + y_S
 avec 
!insmath x_S=\frac{-b}{2a}
 et 
!insmath y_S=f(x_S)
</p>
<table class="wimscenter">
<tr><td></td><td>
!insmath \Delta \lt 0
</td>
<td>
!insmath \Delta = 0
</td><td>
!insmath \Delta \gt 0
</td></tr>
<tr><td>
!insmath a \gt 0
</td>
<td>
!read primitives.phtml 1, draw, 200,200, xrange -2,8	yrange -2,8	arrow -2,0,8,0,8, black	arrow 0,-2,0,8,8, black	dline 0,1,3,1,red	dline 3,0,3,1,red	text red,2.9,-0.1 , large, x	text red,3.4,-0.5, small, S	text red,-1,1.5, large,y	text red,-0.5,1, small, S	plot black,(x-3)^2+1	text black,1.7,4.5, large, f	 

<br>cas 1<br> $m_tab1
 </td><td>

!read primitives.phtml 2, draw, 200,200, xrange -2,8	yrange -2,8	arrow -2,0,8,0,8, black	text red,2.9,-0.1,large,x	text red,3.4,-0.5,small,S	plot black, (x-3)^2	text black1.7,4.5, large, f	 

<br>cas 2<br>$m_tab2
 </td><td>

!read primitives.phtml 3, draw, 200,200, xrange -2,8	yrange -5,5	arrow -2,0,8,0,8, black	arrow 0,-5,0,5,8, black	dline 0,-2,3,-2,red	dline 3,0,3,-2,red	text red,2.9,1,large, x	text red,3.4,0.6,small, S	text red,1.1,-0.1,large, x	text red,1.6,-0.6,small, 1	text red,4.5,-0.1,large, x	text red,5,-0.6,small, 2	text red,-1,-1.5,large,y	text red,-0.5,-2,small, S	plot black, (x-3)^2-2	text black,1.7,1.5,large, f	 

<br>cas 3<br>$m_tab3
</td></tr>
<tr><td>
!insmath a \lt 0
</td><td>

!read primitives.phtml 4, draw, 200,200, xrange -2,8	yrange -8,2	arrow -2,0,8,0,8, black	arrow 0,-8,0,2,8, black	dline 0,-1,3,-1,red	dline 3,0,3,-1,red	text red,  2.9,1 , large, x	text red,  3.4,0.6, small, S	text red,  -1,-0.5, large,y	text red,  -0.5,-1, small, S	plot black, -(x-3)^2-1	text black,  1.7,-4.5, large, f	 
<br>$m_tab4<br>cas 4
 </td><td>

!read primitives.phtml 5, draw, 200,200, xrange -2,8	yrange -8,2	arrow -2,0,8,0,8, black	text red,  2.9,1 , large, x	text red,  3.4,0.6, small, S	plot black, -(x-3)^2	text black,  1.7,-4.5, large, f	 

<br>$m_tab5<br>cas 5
 </td><td>

!read primitives.phtml 6, draw, 200,200, xrange -2,8	yrange -5,5	arrow -2,0,8,0,8, black	arrow 0,-5,0,5,8, black	dline 0,2,3,2,red	dline 3,0,3,2,red	text red,  2.9,-0.1, large, x	text red,  3.4,-0.6, small, S	text red,  1.6,-0.1 , large, x	text red,  2.1,-0.6, small, 2	text red,  4,-0.1 , large, x	text red,  4.5,-0.6, small, 1	text red,  -1,2.5, large,y	text red,  -0.5,2, small, S	plot black, -(x-3)^2+2	text black,  1.7,-1.5, large, f	 

<br>$m_tab6<br>cas 6
</td>
</tr>
<tr><td>Racines<br>Solutions de<br>
!insmath f(x) = 0
</td><td>Pas de racine.</td><td>
!insmath x_S = x_1 = x_2 = \frac{-b}{2 a}
</td><td>
!insmath x_1=\frac{-b-\sqrt{\Delta}}{2 a}
 et 
!insmath x_2=\frac{-b+\sqrt{\Delta}}{2 a}
</td></tr>
<tr><td>Factorisation</td><td>Pas de factorisation</td><td>
!insmath f(x) = a (x - x_S)^2
</td><td>
!insmath f(x) = a (x - x_1) (x - x_2)
</td></tr>
</table>

