Interactive graphing tool problem that asks the student to plot a cubic.
Download file: GraphToolCubic.pg
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
Statement
This asks to graph the cubic throw the given points. 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 by evaluating [`p(0)=[$y0]`], then select [`(0,[$y0])`]. The solution is [@ $gt->generateAnswerGraph @]* END_PGML_SOLUTION ENDDOCUMENT();
Solution
The solution describes how to obtain the graph of the circle from the equation.