Solver Plot a parabola and a tangent to it

Source code of 'Plot a parabola and a tangent to it'

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==section input
For a parabola given by equation y = *[input a=1]x<SUPER>2</SUPER> + *[input b=2]x + *[input c=-3], plot its graph and a tangent at the point of x= *[input x=2]

==section solution
perl

my $y = $a*$x*$x+$b*$x + $c;
$slope = 2*$a*$x+$b;
$d = $y - $slope * $x;

print "A tangent to a parabola {{{y=$a x^2 + $b x + $c}}} is 
a straight line that goes through a particular point of the 
parabola and has the same slope as the parabola.

For the value of x given as $x, we have to calculate y.

{{{y=$a x^2 + ($b x) + ($c) = $y}}}.

So, we know that the point of the tangent is ($x, $y).

The slope of the parabola is {{{slope = 2ax+b = 2*$a x + $b = $slope}}}.

So, now we need to find an equation of a line that goes through 
point ($x, $y) and has slope of $slope. Since the slope is the 
coefficient in front of x, and we already know it, we have to find 
equation of a line

{{{y=$slope x + d}}}

Given that for x=$x, y=$y, we have: $slope x + d = $y. So, d = $y - $slope * $x = $d.

We need to plot parabola {{{y=$a*x^2 + ($b*x) +($c)}}} and line {{{y=$slope*x + $d}}}.

{{{graph( 600, 400, -10, 10, -10, 10, y=$a*x^2 + ($b*x) +($c), $slope*x + ($d) ) }}}
";

==section output
  slope
  d
==section check
 a=1 b=2 c=-3 x=2 d=-7 slope=6