DOCUMENT();

loadMacros(
  "PGstandard.pl",
  "PGML.pl",
  "MathObjects.pl",
  "contextArbitraryString.pl",
  "parserPopUp.pl",
  "parserImplicitEquation.pl",
  "parserMultiAnswer.pl",
  "parserFunction.pl"
);

$x_intercept1 = random(2,7);
$x_intercept2_num = 1;
$x_intercept2_den = random(2,7);
$x_intercept2 = $x_intercept2_num/$x_intercept2_den;

$a = $x_intercept2_den;
$b = -($x_intercept2_den*$x_intercept1 + $x_intercept2_num);
$c = $x_intercept1*$x_intercept2_num;

if (random(0,1,1) == 0) {
  $a = -$a;$b = -$b;$c = -$c;
  $direction = "a downwards";
  $minmax = "maximum";
} else {
  $direction = "an upwards";
  $minmax = "minimum";
}

$popup1 = DropDown(
  ['an upwards', 'a downwards'],
  $direction,
  placeholder => 'Select One'
);

$popup2 = DropDown(
  ['line', 'curve', 'sinusoidal wave', 'circle', 'hyperbola', 'parabola', 'ellipse'],
  'parabola',
  placeholder => 'Select One'
);

$popup3 = DropDown(
  ['minimum', 'maximum'],
  $minmax,
  placeholder => 'Select One'
);

Context()->noreduce('(-x)+y','y-x');
$f = Formula("$a x^2 + $b x + $c")->reduce;

BEGIN_PGML

Define the function [`f`] by [`f(x) = [$f]`].

----

Describe the graph of [`f`].

**Answer:** The graph of [`f`] is [_]{$popup1} facing [_]{$popup2}.

----

END_PGML

Context("ImplicitEquation");

Context()->variables->set(
  x => { limits => [-100,100] }
);

$symmetry = -$b/(2*$a);

$axis = ImplicitEquation("x = $symmetry");

BEGIN_PGML

Find the axis of symmetry and express it as an equation.

**Answer:** [_]{$axis}

----

END_PGML

Context("Point");

Context()->variables->are( x => 'Real');
parserFunction('f(x)' => $f);

$vertex_x = $symmetry;
$vertex_y = $f->substitute(x => "$symmetry")->eval();
$vertex = Compute("($vertex_x,f($vertex_x))");

BEGIN_PGML

Find the vertex of [`f`], and express it as a point.

**Answer:** [_]{$vertex}

----

END_PGML

Context("Interval");
Context()->variables->are( x => 'Real');
parserFunction('f(x)' => $f);

if ($a > 0) {$range = Interval("[$vertex_y,infinity)");}
else {$range = Interval("(-infinity, $vertex_y]");}

BEGIN_PGML

What is the range of [`f(x)`]?

**Answer:** [_]{$range}

----

END_PGML

Context("Numeric");

$intercepts = MultiAnswer($x_intercept1, $x_intercept2)->with(
  singleResult => 0,
  checker => sub {
    my ($correct, $student, $self) = @_;
    my ($x1stu, $x2stu) = @{$student};
    my ($x1, $x2) = @{$correct};
    
    if (($x1 == $x1stu && $x2 == $x2stu) || ($x1 == $x2stu && $x2 == $x1stu)) {
      return [1,1];
    } elsif ($x1 == $x1stu || $x2 == $x1stu) {
      return [1,0];
    } elsif ($x1 == $x2stu || $x2 == $x2stu) {
      return [0,1];
    } else {
      return [0,0];
    }
  }
);

BEGIN_PGML

What are the [`x`]-intercepts of the graph of [`f`]?

**Answer:** [`x = `] [_]{$intercepts} and [`x = `] [_]{$intercepts}

END_PGML
ENDDOCUMENT();