Maximum and Minimum

Rewrite the equation by the order of powers.

This is a parabola in standard form:

Determine the values of to the vertex formula.

Since the leading coefficient of the parabola is negative, the parabola will curve downward and will have a maximum point.

Therefore there is a maximum at,

.

The equation of a parabola can be written in vertex form

where is the vertex and determines if it is a minimum or maximum. If is positive, then it is a minimum; if is negative, then it is a maximum.

In this example, is negative, so the vertex is a maximum.

and