The parabola with equation
y=a(x−2)(x+4) crosses the x-axis at the points
0(−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).
Thus, the x-coordinate of the vertex is
=−1.
This is the value of c. To 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
Therefore, the value of d is
−9a.Choice B is incorrect because the value of the constant term in the equation is not the y-coordinate of the vertex, unless there were no linear terms in the quadratic.
Choice C is incorrect and may be the result of a sign error in finding the x-coordinate of the vertex.
Choice D is incorrect because the negative of the coefficient of the linear term in the quadratic is not the y-coordinate of the vertex