Cubic and Quadratic Graphs

Investigate the behavior of linear, quadratic and cubic graphs in the form y = Ax³ + Bx² + Cx + D and their equations, in this interactive Java applet. Challenge yourself to find the equation of a randomly drawn graph.

Author and programmer: Ron Barrow

UK Years 12-13, Ages 16-19, KS5, Core AS and A2 Mathematics - Functions and Graphs
US Grades 11, 12 - Algebra I and Algebra II


Instructions below   See also:  Polynomial Transformations   Solving Cubic Equations

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How to Use this Applet

The applet on this page is designed to help you understand the behaviour of polynomial (cubic, quadratic and linear) graphs.
The general cubic has the form: y = Ax³ + Bx² + Cx + D.
The general quadratic is: y = Bx² + Cx + D.
The general linear is: y = Cx + D.
These curves are drawn in white and their equations given at the top left. Varying A, B, C and D changes the curves. (Note that if you're in quadratic mode, A no longer is relevant, so clicking it will have no effect. Similarly, in linear mode A and B are not used.)

Try to get a feel for what happens when you press the buttons. You might wish to start with straight lines (linear) or quadratics, then move on to cubics. Playing around will deepen your understanding of these important functions.
Challenge - Clicking the "Random Curve" button will draw a random graph in yellow. By clicking the A, B, C and D buttons, try to cover the yellow graph with the white one. (The cubic is hard!)
Enjoy playing around!