What are the vertex and x intercepts of the graph of the function below y=(x-4)(x+2)

see explanation

Step-by-step explanation:

To find the x- intercepts let y = 0, that is

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

Equate each factor to zero and solve for x

x - 4 = 0 ⇒ x = 4

x + 2 = 0 ⇒ x = - 2

x- intercepts are x = - 2 and x = 4

The vertex lies on the axis of symmetry which is located at the midpoint of the x- intercepts, thus

= = 1

Substitute x = 1 into the equation for corresponding value of y

y = (1 - 4)(1 + 2) = - 3 × 3 = - 9

vertex = (1, - 9)

77

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