Quadratic graphs

A quadratic graph is produced when you have an equation of the form y = ax^2 + bx + c, where b and c can be zero but a cannot be zero.

All quadratic graphs have a line of symmetry.

Positive quadratic graphs (where a \textgreater 0) are U-shaped and have a minimum turning point.

Negative quadratic graphs (where a \textless 0) are \cap-shaped and have a maximum turning point.

The graph of the quadratic function y = ax^2 + bx + c has a minimum turning point when a > 0 and a maximum turning point when a < 0. The turning point lies on the line of symmetry.

Plotting a quadratic graph

Example

Draw the graph of y = x^2 – x – 4

Solution

First we need to complete a table of values:

x-3-2-1012345
y82-2-4-4-22816

Then plot these points and join them with a smooth curve.

Graphic of plotting points on a graph sketch from a table of values