Question

The quadratic function f(x) has roots at x=4 and x=-2 and has value of 2 at x=0. Does f(x) have a minimum or maximum?

Find the value of the /minimum/maximum value of f(x).

Answer 1

f(x)=a(x-4)(x+2)
2=a(-4)(2)
a=-1/4

f(x)=-1/4 (x-4)(x+2)
f'=-1/4(x-4)-1/4(x+2)=0
-x+4-x-2=0
x=1 max or min
f"=-2/4 so it is curving down, it is a max at x=1