Recognising Quadratic, Cubic and Reciprocal Graphs

With this applet you can learn how to recognise basic quadratic, cubic and reciprocal graphs

UK Years 10-11, Ages 14-16, KS4, GCSE Mathematics - Algebra, Graphs

Instructions below    A smaller version of this applet    See also:  Cubic and Quadratic Graphs    Reciprocal (Rational Graphs)

[Applet - Simple Quadratic, Cubic and Reciprocal Functions]

The screen above is designed to help you recognise and understand some simple functions, by investigating their behaviour. The are three types of function for you to study:
y = ax² + b - quadratic, since it involves x²
y = ax³ + b - cubic, since it involves x³
y = a/x + b - sometimes called the reciprocal function

In each case you should recognise the general shape of the function, and you can use this applet to investigate the effects of changing the 'a' and 'b' values.
A challenge! You can also test yourself by pressing the "Random Curve" button. This draws a curve of one of the 3 types (but doesn't tell you which!) Your first task is to decide which type it is, then try to match it by varying 'a' and 'b' values. Best of luck! Have fun!