Question

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

Answer 1

Explanation:

x + 4 = 0

x = -4

(-4, 0)

x - 2 = 0

x = 2

(2, 0)

x^2 + 2x - 8

-2/2 = -1

(-1)^2 - 2 - 8

1 - 2 - 8 = -1 - 8 = -9

(-1, -9) is the vertex

Answer 2

• vertex: (-1, -9)
• x-intercepts: (-4, 0) and (2, 0)

Explanation:

You want the vertex and x-intercepts of the graph of the function y = (x +4)(x -2).

X-intercepts

The x-intercepts are the values of x that make the function be zero. That will be the case when either factor is zero. Thus, the x-intercepts are the values of x that make the factors zero:

x +4 = 0 ⇒ x = -4

x -2 = 0 ⇒ x = 2

The x-intercepts are (-4, 0) and (2, 0).

Vertex

The vertex is the point on the graph that lies on the line of symmetry. That line is halfway between the x-intercepts, at ...

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

The y-value there is ...

y = (-1 +4)(-1 -2) = (3)(-3) = -9

The coordinates of the vertex are (x, y) = (-1, -9).

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