Graph Tool, plotting a cubic

Interactive graphing tool problem that asks the student to plot a cubic.

Complete Code

POD for Macro Files

PG problem file

Explanation

DOCUMENT();

loadMacros(
    'PGstandard.pl',      'PGML.pl',
    'parserGraphTool.pl', 'contextFraction.pl',
    'PGcourse.pl'
);

Preamble

This example shows how to get student input in the form of a graph (a cubic) by using interactive graphing tools. Load the parserGraphTool.pl macro for this.

Context('Fraction');

$x1 = random(-8, -4);
$x2 = non_zero_random(-3, -3);
$x3 = random(4, 8);

$y0 = non_zero_random(-3, 3);

$k = Fraction($y0, -$x1 * $x2 * $x3);

$gt =
    GraphTool("{cubic, solid, ($x1, 0), ($x2, 0), ($x3, 0), (0, $y0)}")->with(
        bBox           => [ -11, 11, 11, -11 ],
        availableTools => [
            'PointTool',  'LineTool',
            'CircleTool', 'QuadraticTool',
            'CubicTool',  'FillTool',
            'SolidDashTool'
        ],
    );

Setup

A cubic is created with 3 random zeros and a random y-intercept.

The GraphTool method creates the graph tool object. The only argument is the correct answer. This is a string that contains a list of objects that the student will be expected to graph. Each object is a brace delimited list of the attributes of the object. The first attribute in each list is the type of object to be graphed, cubic in this case. What the remaining attributes are depend on the type. For a cubic the second attribute is whether the object is to be solid or dashed, the remaining attributes are four distinct points of the cubic.

The ->with method is then used to set options for the GraphTool object. In this case the options that are set are:

bBox: This is an array reference of four values xmin, ymax, xmax, ymin indicating the upper left and lower right corners of the visible graph.
availableTools: This determines which tools will be available for the student to use.

There is a default checker for the GraphTool that will mark correct a student answer that ‘looks’ like the correct one. For simple graphs, the default should be sufficient. See Graph Tool, custom checker for an example of how to use a custom checker.

BEGIN_PGML
Graph the cubic function [``p(x) = [$k](x-[$x1])(x-[$x2])(x-[$x3])``]

[_]{$gt}
END_PGML

$altText = 'the graph of a cubic function through the points '
    . "($x1, 0), ($x2, 0), ($x3, 0), and (0, $y0)";

Statement

This asks to the student to graph the cubic defined by the given equation. The code [_]{$gt} inserts the GraphTool.

BEGIN_PGML_SOLUTION
To graph the cubic, you'll need 4 points.  Because of the form, there are 3
zeros [`([$x1], 0)`], [`([$x2], 0)`] and [`([$x3], 0)`].  Any other point can be
chosen, but another easy one is the [`y`]-intercept, which can be found by
evaluating [`p(0) = [$y0]`], then select [`(0, [$y0])`].

The solution is
[![$altText]!]{$gt}
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

The solution describes how to obtain the graph of the circle from the equation.