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 \(a \textless 0\)) are \(\cap\)-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 complete a table of values:

\(x\)	-3	-2	-1	0	1	2	3	4	5
\(y\)	8	2	-2	-4	-4	-2	2	8	16

\(x\)
-3
-2
-1
0
1
2
3
4
5

\(y\)
8
2
-2
-4
-4
-2
2
8
16

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

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

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