Given y=a(x−2)(x+4). In the given quadratic equation, aa is a nonzero constant. The graph of the equation in the xy-plane is a parabola with vertex (c,d). Which of the following is equal to d?

# Given y=a(x−2)(x+4). In the given quadratic equation, aa is a nonzero constant. The graph of the equation in the xy-plane is a parabola with vertex (c,d). Which of the following is equal to d?

1. A
-9a
2. B
-8a
3. C
-5a
4. D
-2a

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### Solution:

The parabola with equation y=a(x−2)(x+4), crosses x axis at the points (−4,0) and (2,0).
The x coordinate of the vertex of the parabola is halfway between the x coordinates of (−4,0) and (2,0).
Therefore, the x coordinate of the vertex is  2−4+2​=−1
This is the value of c.We will find the y coordinate of the vertex, substitute −1 for x in y=a(x−2)(x+4):
y=a(x−2)(x+4)=a(−1−2)(−1+4)=a(−3)(3)= −9a
Hence, Option (1) is the correct answer.

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