Question

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

Answer 1

(2,-16) should be the answer

Answer 2

vertex = (2, - 16)

Explanation:

given

f(x) = (x - 6)(x + 2) ← equate to zero to find the zeros

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

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 2 = 0 ⇒ x = - 2

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

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

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

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

vertex = (2, - 16)