Solver Convert to Vertex Form and Graph

Source code of 'Convert to Vertex Form and Graph'

This Solver (Convert to Vertex Form and Graph) was created by by ccs2011(207)

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==section input

Enter quadratic equation in standard form:
--> *[input a=a] x<SUP>2</SUP> + *[input b=b] x + *[input c=c]

==section solution
perl
if ($a == 0) {
   print "Sorry, that is not a valid quadratic equation.\n Please try again\n";
   return;
}

my $mid = $b/$a;
my $h = $mid/2;
my $sq = $h*$h;
my $c1 = $a*$sq;
my $k = $c - $c1;
my $x0 = -$h;

my ($txt,$x1,$x2,$y1,$y2);

if ($a < 0) {
 $txt = down;
 $x1 = $x0 - 10;
 $x2 = $x0 + 10;
 $y1 = $k -25;
 $y2 = $k + 1;
}else {
 $txt = up;
 $x1 = $x0 - 10;
 $x2 = $x0 + 10;
 $y1 = $k -1;
 $y2 = $k + 25;
}

print "--> {{{$a*x^2 + ($b)*x + ($c)}}} \n\n";
print "\n Step 1: Group the first 2 terms together, separating them from the constant term.\n\n";
print "\n -->{{{($a*x^2 + ($b)*x) + ($c)}}} \n\n";
print "\n Step 2: Factor out leading coefficient, for completing the square to work, the coefficient of x<SUP>2</SUP> must be 1.\n\n";
print "\n -->{{{$a(x^2 + ($mid)*x) + ($c)}}}\n\n";
print "\n Step 3: Complete the square, Take half of x coefficient and square it. Notice to keep equation balanced you must add this number and subtract it making the net effect zero.\n\n";
print "\n --> {{{$a(x^2 + ($mid)*x + $sq - $sq)+ ($c)}}}\n\n";
print "\n --> {{{$a((x+($h))^2 - $sq)+ ($c)}}}\n\n";
print "\n Step 4: Distribute and add constants.\n\n";
print "\n --> {{{$a(x+($h))^2 -$c1 + $c}}}\n\n";
print "\n --> {{{$a(x+($h))^2 + ($k)}}}\n\n";
print "\n Now it is successfully in vertex form and can be easily graphed.\n
The vertex is at ($x0,$k)\n
The parabola opens $txt and has a y-intercept at (0, $c)\n
Here is a graph of this parabola: \n\n 
{{{graph(300,300,$x1,$x2, $y1, $y2, $a*x^2+($b)*x+$c)}}}";

==section output
x
==section check
 = = =

a=1 b=0 c=0 k=0