Question

Please solve this question..​

Answer 1

vertex = (- 1, - 4.5 )

Explanation:

Given

f(x) =
`(1)/(2)` (x - 2)(x + 4)

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

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

`(1)/(2)` (x - 2)(x + 4) = 0

Equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x + 4 = 0 ⇒ x = - 4

The x- coordinate of the vertex is therefore

x =
`(-4+2)/(2)` =
`(-2)/(2)` = - 1

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

f(- 1) =
`(1)/(2)` (- 1 - 2)(- 1 + 4) =
`(1)/(2)` × - 3 × 3 = 0.5 × - 9 = - 4.5

Coordinates of vertex = (- 1, - 4.5 )