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.
