Question

What is the y-value of the vertex of the function f(x)=-(x-3)(x+11)?

Answer 1

49

Explanation:

The vertex lies on the axis of symmetry which is situated at the midpoint of the zeros.

Find the zeros by letting f(x) = 0, that is

- (x - 3)(x + 11) = 0

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x + 11 = 0 ⇒ x = - 11, thus

`x_(vertex)` =
`(-11+3)/(2)` =
`(-8)/(2)` = - 4

Substitute x = - 4 into f(x) for y- value of the vertex

f(- 4) = - (- 4 - 3)(- 4 + 11) = - (- 7)(7) = 49