Explanation:
This is a family of curves represented by the equation:
y = a (x + 4) (x − 2)
Different values of the a coefficient result in different quadratic functions.
The vertex of the parabolas is halfway between the zeros, at x = -1.
y = a (-1 + 4) (-1 − 2)
y = -9a
So to find the value of a, divide the y-coordinate of the vertex by -9. For example, curve A has a vertex at (-1, -3), so the value of the a coefficient is -3 / -9 = ⅓.
A. y = ⅓ (x + 4) (x − 2)
B. y = (x + 4) (x − 2)
C. y = 2 (x + 4) (x − 2)
D. y = -⅓ (x + 4) (x − 2)
E. y = -2 (x + 4) (x − 2)