Answer:
- 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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