Question

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

Answer 1

x - intercepts: (4,0) and (-2,0)

vertex: (1/2 , - 17/2)

Explanation:

Part A

To find the x-intercepts you have to set y=0

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

Separate the parenthesis. Solve for x

x-4 = 0

x= 4

x+2 = 0

x= -2

x - intercepts: (4,0) and (-2,0)

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Part B

vertex formula for the x: coordinate : -b/2a

Expand the function.

y = 2x^2-2x-8

a = 2

b = -2

c= -8

-b/2a = -(-2)/2(2) = 1/2

vertex x- coordinate: 1/2

Substitute 1/2 back into every "x" in the function to find the "Y" for the vertex.

y = 2(1/2)^2 -2(1/2) -8

y = -17/2

vertex: (1/2 , - 17/2)