Question

Find the vertex of the quadratic function f(x) = (x-4) (x+2)

Answer 1

vertex = (1, - 9 )

Explanation:

The x- coordinate of the vertex is at the midpoint of the zeros.

Given

f(x) = (x - 4)(x + 2)

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

(x - 4)(x + 2) = 0

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 4 = 0 ⇒ x = 4

Then

`x_(vertex)` =
`(-2+4)/(2)` =
`(2)/(2)` = 1

Substitute x = 1 into f(x) for corresponding y- coordinate

f(1) = (1 - 4)(1 + 2) = (- 3)(3) = - 9

Vertex = (1, - 9 )