Question

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

Answer 1

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: `(-2+4)/2`=1.

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