Question

What is the vertex of the quadratic funtion f(x)=(x-6)(x+2)?

Answer 1

vertex = (2, - 16 )

Explanation:

The vertex is positioned midway between the zeros

Given

f(x) = (x - 6)(x + 2)

To find the zeros equate f(x) to zero, that is

(x - 6)(x + 2) = 0

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 2 = 0 ⇒ x = - 2

Thus

`x_(vertex)` =
`(-2+6)/(2)` =
`(4)/(2)` = 2

Substitute x = 2 into f(x) for corresponding y- coordinate

f(2) = (2 - 6)(2 + 2) = (- 4)(4) = - 16

vertex = (2, - 16 )