Find a so that f(x) = ax2 + 4x − 4 has a minimum value of −8.

Answer 1

So since f(x) = ax² + 4x − 4 is a parabola, we are looking for the vertex of the parabola to find its minimum value.

The vertex has the x value of -b/(2a) in this case then x = -4/(2a) = -2/a

To find the minimum value, we need to plug in the x we got for the vertex into the equation

So f(-2/a) = a(-2/a)² + 4(-2/a) − 4 but we know that the minimum value is -8 so:

-8 = a(-2/a)² + 4(-2/a) − 4

-8 = 4/a- 8/a - 4

-4 = -4/a

a = 1