n=$counter
checkfile=exos/checkfile5.proc
R=$level
!if $level=0
    R=$counter
!endif    
var1=a
var2=b
var3=c
!if $R=1 or $R=2
    a=!randitem -3,-2,-1,1,2,3
    b=!randitem -6,-5,-4,-3,-2,-1,1,2,3,4,5,6
    c=!randitem 1,2,3,4,5,6,7,8,9,10
    x2=0
    y2=$c
    x1=!randitem -2,-1,1,2,3
!else
    a=!randitem -4,-3,-2,-1,1,2,3,4
    b=!randitem -6,-5,-4,-3,-2,-1,1,2,3,4,5,6
    c=!randitem 5,6,7,8,9,10
    x1=!randitem -2,-1,1,2,3
    x2=!randitem -6,-5,-4,-3,4,5,6
    y2=$[($a)*($x2)^2+($b)*($x2)+($c)]
!endif
    
y1=$[($a)*($x1)^2+($b)*($x1)+($c)]
f=$a*x^2+$b*x+$c
h=$[2*($a)*($x1)+($b)]
function=!htmlmath y=a*x^2+bx+c
ss=!record 19 of lang/remarks.$taal
question$n=$ss
#@ Een parabool met vergelijking<p align="center">$function</p> gaat door het punt ($x2:$y2)<br>In het punt ($x1:$y1) is de helling van de raaklijn aan de parabool <b>$h</b><br>Bereken <b>a</b> , <b>b</b> en <b>c</b>
answer$n=$a,$b,$c
ff=!texmath y = $a*x^2 + $b*x + $c
!if $R=1 or $R=2
    texanswer$n=\left[ \begin{array}{l} ($x2 : $y2) \rightarrow c = $y2 \\ \\ \frac{dy}{dx} = 2ax+b \\ \\ (I)\,\, ($x1 : $y1) \rightarrow  $x1 \cdot 2a  + b = $h \rightarrow b = $h - $[2*$x1] a \\  \\(II) \,\, $y1=a ( $x1 )^{2} + b \cdot $x1 + $y2 \rightarrow $[$x1^2] a + $x1 b = $[$y2-$y1]  \\  \\ ( I \,\, in \,\, II ) \,\, $[$x1^2] a + $x1 ( $h - $[2*$x1] a) = $[$y2-$y1] \\  \\ \longrightarrow $ff \end{array} 
!else
    texanswer$n=$ff
!endif
textanswer$n=<ul><li>a=$a</li><li>b=$b</li><li>c=$c</li></ul>
exotext=!record 25 of lang/remarks.$taal
sometext=!record 26 of lang/remarks.$taal
exotext=<p><a onmouseover="return escape('$sometext')">$exotext
helptext=$empty
