Question

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

The y-value of the vertex is

.

Answer 1

49

Explanation:

Given

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

Find the zeros by setting 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

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

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

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

f(- 4) = -(- 7)(7) = 49 ← y- value of vertex