# Quadratic functions - Domains, ranges and Inverses

This applet investigates the domain and range of a quadratic function, and how its domain needs to be restricted in order for it to become one-to-one (one-one), so that an inverse function exists. See how this function and its inverse are related on the graph.

###### Author and programmer: Ron Barrow

UK Years 12-13, KS5, KS4, Core 3 (C3) GCE Mathematics, Algebra and Functions

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See also:
Quadratics: Completing the Square
Quadratics:The Discriminant

Quadratic Inequalities
Modulus Functions

## How to Use this Applet

This applet is designed to help you understand inverse functions, and their domains and ranges, by looking at quadratic graphs. There are three drag-boxes at the bottom of the screen. Clicking in these boxes and then dragging left or right to enable you to change the values of a, b and c. This will change the graph, which is `y` = a`x`² + b`x` + c. The "Reset" button returns you to the beginning, `y` = `x`². The two dots at the ends of the `x`-axis can be dragged with your mouse. This restricts the domain of the function. If the dots are at the ends of the axes then they are considered to be at infinity. If the "Inverse" box is checked then when the function is one-to-one an inverse function will be drawn. Notice how the domain and range of the inverse are related to those of the original function, and how they are both related on the graph. Play around!