# 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

TweetInstructions below See also: Polynomial Graphs

## How to Use this Applet

The general cubic equation has the form:

`y` = A`x`³ + B`x`² + C`x` + 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!