The Graph of y² = f(x)

This applet investigates what happens if you plot y² = f(x) alongside y = f(x). It uses a cubic graph as f(x), but you can investigate the general behaviour of the function y² = f(x) for any single-valued function using this applet. You should notice the behaviour as f(x) just touches the x-axis, as it crosses the x-axis, and as it crosses the line y = 1.

Author and programmer: Ron Barrow

UK Year 13, Ages 17-19, KS5, A2 Further Mathematics FP2 - Calculus, Functions and Graphs

   
           

Instructions below   See also:  Polynomial Graphs

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How to Use this Applet

The general cubic equation has the form:
y = Ax³ + Bx² + Cx + D.
The equation of y = f(x) is given at the top left. Varying A, B, C and D changes this curve.

The equation of y² = f(x) is given at the top right.
You hide or show either of the two graphs, and the line y = 1, using the checkboxes at the top.
Enjoy playing around!