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)

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5