Maximum and Minimum Values

Working Towards a Solution

The vertex is either a maximum or minimum point on the graph. The following is a description of how to analyze a function and tell whether there is a maximum or minimum value.

Let f(x) = ax² + bx + c, where a ≠ 0.

If a > 0 the graph opens up and the vertex is the minimum value.
If a < 0 the graph opens down and the vertex is the maximum value.

For example, the following is the graph of f(x) = x² – 1.

Graph of f(x) = x² – 1

Since a is equal to one, which is of course greater than zero, the function opens upward and the vertex will be a minimum value.

Next: Section F, page 9

© 2009 KC Distance Learning. All rights reserved.