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

  D.  y = -x^2+4x-4

Step-by-step 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

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step-by-step explanation:

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