Question

What is the vertex of the quadratic function? f(x)= (x-8)(x-4)

Answer 1

C

Explanation:

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

Given

f(x) = (x - 8)(x - 4)

To find the zeros let f(x) = 0, that is

(x - 8)(x - 4) = 0

Equate each factor to zero and solve for x

x - 8 = 0 ⇒ x = 8

x - 4 = 0 ⇒ x = 4

Thus

`x_(vertex)` =
`(8+4)/(2)` =
`(12)/(2)` = 6

Substitute x = 6 into f(x) for corresponding y- coordinate of vertex

f(6) = (6 - 8)(6 - 4) = (- 2)(2) = - 4

Vertex = (6, - 4 ) → C

Answer 2

the vertex is A. (4,8)