# How do you find the maximum and minimum of y=(x+2)(x-4)?

Aug 22, 2017

A quadratic equation will have either a maximum or a minimum, but not both.

#### Explanation:

This function, y = (x+2)(x - 4) has to "zeros" where the graph crosses the x-axis. Look at the picture below:

Notice that halfway in between the two zeros, the graph reaches its lowest point at the "vertex". The y-value here will be the minimum value. Let's find the y-value.

Average the two zeros: $\frac{- 2 + 4}{2}$=1.

Substitute x = 1 into the equation: y = (1+2)(1-4) = $3 \cdot - 3$ = -9.
Your vertex is at (1, -9) and the minimum value is -9.