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

1 Answer
Aug 22, 2017

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


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

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.