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 turning point at the bottom of the curve. Negative quadratic graphs (where \( a \textless\)) are ∩-shaped and have a turning point at the top of the curve.

A graph showing the turning point when a > 0 and 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
\[y\]82-2-4-4-22816

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

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