!if $rounding=-1
    rounding=100
    !readproc $remarkdir/rounding.$taal
!endif
n=$counter
image=0
XSIZE=650
questiontype=0
inputs=2
rows=5
cols=20
draw=1
plot=0
math=0
varlist=x
!if $level=0
    R=$counter
!else
    R=$level
!endif

checkfile=exos/checkfile1.proc 
l=<font size="+1" color=green><em>l</em></font>
p=<font size="+1" color=red><em>p</em></font>
keuze=!randitem groter,kleiner
boven=!record 40 of lang/remarks.$taal
#@ de parabool $p boven de lijn $l ligt.
onder=!record 41 of lang/remarks.$taal
#@ de parabool $p onder de lijn $l ligt.
exotext=!record 53 of lang/remarks.$taal
#@ <p align="left"><small>** Let op voor de "speciale" schrijfwijze van<ul><li>Voor x&ge;5 <font color=$fontcolor3>moet</font> je invullen x&gt;=5 (5&lt;=x)</li><li>Voor x&le;5 <font color=$fontcolor3>moet</font> je invullen x&lt;=5 (5&gt;=x)</li><li>Voor 2&le;x&le;5 <font color=$fontcolor3>mag</font> je invullen 2&lt;=x&lt;=5<br>of  2&lt=x en x&lt;=5 <br> of  x&gt;=2 en x&lt;=5 <br> of alle variaties hierop...</li><li>noteer co&ouml;rdinaten als (x;y) of (x:y) en  geen komma ertussen</li></small></ul>
sometext2=!record 39 of lang/remarks.$taal
inputtext1=!item 1 of $sometext2
inputtext2=!item 2 of $sometext2

!if $R=1
    a=!randitem 1,3,5,7,9
    b=!randitem 0,2,4,6,8    
    c=!randitem 1/2,1/4,1/3,2/3,6/7,7/4,9/4,13/4,3/4,2/5,3/5,5/6,5/8,7/8,9/10,1,2,3/2,4/5,3,4,5,6
    e=!randitem -1,1
    c=!exec pari $e*$c
    d=!exec pari $a*$b - ($c)
    p1=x^2 + $[$b-$a]*x -$d    
    l1=$c
    P1=!texmath $p1
    L1=!texmath $l1
    x1=$a
    x2=$[-1*$b]
    y1=$c
    y2=$c
    var1=$x1,$y1,$x2,$y2
    !if $rounding>0
	x1=$[(round($rounding*$x1))/$rounding]
	x2=$[(round($rounding*$x2))/$rounding]
	y1=$[(round($rounding*$y1))/$rounding]
	y2=$[(round($rounding*$y2))/$rounding]
    !else
	x1=$x1
	x2=$x2
	y1=$y1
	y2=$y2
    !endif
    !if $keuze=groter
	ligging=$boven 
	var2=x<$x2&&x>$x1
	GG=x<$x2 \vee x>$x1
	ongelijkheid=x &lt; $x2 V x &gt; $x1
	latextekst=<font color=$fontcolor3><b><em>p</em></b></font> &gt; <font color=$fontcolor4><b><em>l</em></b></font>
	LATEXTEKST=p > l
    !else
	ligging=$onder 
	var2=$x2<x&&x<$x1
	GG=$x2<x<$x1
	ongelijkheid=$x2 &lt; x &lt; $x1
	latextekst=<font color=$fontcolor3><b><em>p</em></b></font> &lt; <font color=$fontcolor4><b><em> l</em></b></font>
	LATEXTEKST=p < l
    !endif
    !if $teaching=1
	xrange=-10,10
	yrange=-40,40
        grafiek=linewidth 2\
        curve red,$p1\
        curve green,$l1\
        linewidth 6\
        points yellow,$[$x1],$[$y1],$[$x2],$[$y2]\
        text black,7,-0.5,normal,x-axis\	
        textup black,-0.5,15,normal,y-axis
    !endif
    answer$n=($x1:$y1) ($x2:$y2),$var2
!goto READY
!endif
!if $R=2
    b=!randitem 2,3,4,5,6,7,-2,-3,-4,-5,-6,7
    a=!randitem 2,3,4,5,-1,-2,-3,-4,-5
    c=!randitem 4,6,8,10,12,-4,-6,-8,-10,-12
    pm=!randitem +,-
    x1=!randitem -6,-5,-4,-3,-2,-1
    x2=!randitem 1,2,3,4,5,6
    y1=$[$a*$x1*$x1 $pm $b*$x1 - ($c) ]
    y2=$[$a*$x2*$x2 $pm $b*$x2 - ($c) ]
    p1=!rawmath $a*x^2 $pm $b*x - $c
    P1=!texmath $p1

    tussen=!exec pari ((($y1)-($y2))/(($x1)-($x2)))*x + ($y1) -($x1)*(($y1)-($y2))/(($x1)-($x2))\
    printtex((($y1-$y2)/($x1-$x2))*x + $y1 -$x1*($y1-$y2)/($x1-$x2)) 
    l1=!line 1 of $tussen
    L1=!line 2 of $tussen

    !if $rounding!=0
	x1=$[(round($rounding*$x1))/$rounding]
	x2=$[(round($rounding*$x2))/$rounding]
	y1=$[(round($rounding*$y1))/$rounding]
	y2=$[(round($rounding*$y2))/$rounding]
    !else
	x1=$x1
	x2=$x2
	y1=$y1
	y2=$y2
    !endif
    var1=$x1,$y1,$x2,$y2
    !if $a>0
	!if $keuze=groter
	    ligging=$boven
	    var2=x<$x1&&x>$x2
	    GG=x<$x1 \vee x>$x2
	    ongelijkheid=x &lt; $x1 V x &gt; $x2
	    latextekst=<font color=$fontcolor3><b><em>p</em></b></font> &gt; <font color=$fontcolor4><b><em>l</em></b></font>
	    LATEXTEKST=p > l
	!else
	    ligging=$onder
	    var2=$x1<x&&x<$x2
	    GG=$x1<x<$x2
	    ongelijkheid=$x1 &lt; x &lt; $x2
	    latextekst=<font color=$fontcolor3><b><em>p</em></b></font> &lt; <font color=$fontcolor4><b><em> l</em></b></font>
	    LATEXTEKST=p < l
	!endif
    !else
    	!if $keuze=groter
	    ligging=$boven
	    var2=$x1<x&&x<$x2
	    GG=$x1<x<$x2
	    ongelijkheid=$x1 &lt; x &lt; $x2
	    latextekst=<font color=$fontcolor3><b><em>p</em></b></font> &gt; <font color=$fontcolor4><b><em> l</em></b></font>
	    LATEXTEKST=p > l
	!else
	    ligging=$onder
	    var2=x<$x1&&x>$x2
	    GG=x<$x1 \vee x>$x2
	    ongelijkheid=x &lt; $x1 V x &gt; $x2
	    latextekst=<font color=$fontcolor3><b><em>p</em></b></font> &lt; <font color=$fontcolor4><b><em>l</em></b></font>
	    LATEXTEKST=p < l
	!endif
    !endif
    !if $teaching=1
	xrange=-8,8
        yrange=-300,300
	grafiek=linewidth 2\
	curve red,$p1\
	curve green,$l1\
	linewidth s*14\
	points yellow,$[$x1],$[$y1],$[$x2],$[$y2]\
	text black,5,-5,normal,x-axis\
	textup black,-0.5,200,normal,y-axis
    !endif
    answer$n=($x1:$y1) ($x2:$y2),$var2
!goto READY
!endif

!if $R>2
    b=!randitem 1/2,1/3,1/4,3/4,2/3,4/5,3/5,5/4,7/4,7/5,9/4,13/4
    a=!randitem 1/2,1/3,2/3,1/4,3/4,1/5,-1/4,-2/3,-3/4,-4/5,-5/7,-9/4,13/4
    c=!randitem 4,6,8,10,12,-4,-5,-6,-7,-8,-9,-10,-12
    pm=!randitem +,-
    x1=!randitem -6,-5,-4,-3,-2,-1
    x2=!randitem 1,2,3,4,5,6
    y1=!exec pari $a*$x1*$x1 $pm $b*$x1 - ($c) 
    y2=!exec pari $a*$x2*$x2 $pm $b*$x2 - ($c) 
    p1=!rawmath $a*x^2 $pm $b*x - $c
    P1=!texmath $p1
    tussen=!exec pari ((($y1)-($y2))/(($x1)-($x2)))*x + ($y1) -($x1)*(($y1)-($y2))/(($x1)-($x2))\
    printtex((($y1-$y2)/($x1-$x2))*x + $y1 -$x1*($y1-$y2)/($x1-$x2)) 
    l1=!line 1 of $tussen
    L1=!line 2 of $tussen

    var1=$x1,$y1,$x2,$y2
    !if $a>0
	!if $keuze=groter
	    ligging=$boven
	    var2=x<$x1&&x>$x2
	    GG=x<$x1 \vee x>$x2
	    ongelijkheid=x &lt; $x1 V x &gt; $x2
	    latextekst=<font color=$fontcolor3><b><em>p</em></b></font> &gt; <font color=$fontcolor4><b><em>l</em></b></font>
	    LATEXTEKST=p > l
	!else
	    ligging=$onder
	    var2=$x1<x&&x<$x2
	    GG=$x1<x<$x2
	    ongelijkheid=$x1 &lt; x &lt; $x2
	    latextekst=<font color=$fontcolor3><b><em>p</em></b></font> &lt; <font color=$fontcolor4><b><em> l</em></b></font>
	    LATEXTEKST=p < l
	!endif
    !else
    	!if $keuze=groter
	    ligging=$boven
	    var2=$x1<x&&x<$x2
	    GG=$x1<x<$x2
	    ongelijkheid=$x1 &lt; x &lt; $x2
	    latextekst=<font color=$fontcolor3><b><em>p</em></b></font> &gt; <font color=$fontcolor4><b><em>l</em></b></font>
	    LATEXTEKST=p > l
	!else
	    ligging=$onder
	    var2=x<$x1&&x>$x2
	    GG=x<$x1 \vee x>$x2
	    ongelijkheid=x &lt; $x1 V x &gt; $x2
	    latextekst=<font color=$fontcolor3><b><em>p</em></b></font> &lt; <font color=$fontcolor4><b><em> l</em></b></font>
	    LATEXTEKST=p < l
	!endif
    !endif
    !if $teaching=1
	xrange=-8,8
	yrange=-300,300
        grafiek=linewidth 2\
	curve red,$p1\
	curve green,$l1\
	linewidth s*14\
	points yellow,$[$x1],$[$y1],$[$x2],$[$y2]\
	text black,5,-5,normal,x-axis\
	textup black,-0.5,200,normal,y-axis
    !endif
    answer$n=($x1:$y1) ($x2:$y2),$var2
!endif

:READY

formula$n=\left[ \begin{array}{l}l(x)=$L1\\ \\ p(x)=$P1 \\ \\ $LATEXTEKST \end{array}
texanswer$n=\rightarrow \left[ \begin{array}{l} ($x1 : $y1) \\ ($x2 : $y2) \\ $GG \end{array}\right.

ss=!record 42 of lang/remarks.$taal
question$n=$ss
#@ Gegeven de rechte lijn $l en parabool $p  <br><ul><li>Bepaal de co&ouml;rdinaten van de snijpunten tussen $l en $p </li><li>Geef aan voor welke <em>x</em>-waarden de grafiek van $ligging .</li></ul>
rr=!record 43 of lang/remarks.$taal
textanswer$n=$rr
#@ <p align="left">Het goede antwoord is dus: <ul><li>de snijpunten ($x1:$y1) &and; ($x2:$y2)</li>OP<li>En waar de grafiek van $ligging  geldt:<br> $ongelijkheid</li></ul></p> 

!if $teaching=1
    insdraw_size=320,320
    !insdraw xrange $xrange\
    yrange $yrange\
    linewidth 1\
    vline 0,0,blue\
    hline 0,0,blue\
    $grafiek
        
    helptext=!record 54 of lang/remarks.$taal
    helptext=<a onmouseover="this.T_OPACITY=85;this.T_PADDING=10;this.T_WIDTH=320;this.T_BORDERCOLOR='gold';this.T_BORDERWIDTH=1;return escape('<img src= $wims_refname?&session=$session&module=$module&cmd=getins&special_parm=insert-1.gif>')">$helptext</a>
    #helptext=!record 63 of $remarkdir/commonremarks.$taal
    #helptext=<a href="javascript:showimage();">$helptext
!endif  
    

 
