Question

The vertex of the graph of a function is (2, 0) and the y-intercept is (0, –4). Which of the following could be the equation of the function?

A. y=2x^2-8x-4
B. y=-2x^2+8x-4
C. y=x^2+4x-4
D. y=-x^2+4x-4

Answer 1

D. y = -x^2+4x-4

Explanation:

The y-intercept is lower on the graph than the vertex, so the parabola opens downward. This means the coefficient of x^2 will be negative.

The vertex at (2, 0) means the equation will be of the form ...

y = a(x -h)^2 +k . . . . . for (h, k) = (2, 0)

y = a(x -2)^2 = a(x^2 -4x +4)

Substituting (x, y) = (0, -4), we find ...

-4 = 4a

-1 = a

So, the equation is ...

y = -1(x^2 -4x +4)

y = -x^2 +4x -4 . . . . . . matches selection D