Answer:
vertex = (2, - 16 )
Step-by-step 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
[tex]x_{vertex}[/tex] = [tex]\frac{-2+6}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2
Substitute x = 2 into f(x) for corresponding y- coordinate
f(2) = (2 - 6)(2 + 2) = (- 4)(4) = - 16
vertex = (2, - 16 )
