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 = 22² - 8x - 4
B. y=-2x² + 8x - 4
C y =x2 – 3x + 2
D. y=-x? +4x-4

Correct D.  y = - x² + 4 x - 4

Step-by-step explanation:

Given:

Vertex (2, 0) = (α, β)

y-intercept (0, -4) = (x, y)

Vertex form of quadratic equation is:

y = a (x - α)² + β

We will first replace the given coordinates of the vertex

y = a · (x - 2)² + 0 = a · (x - 2)²

y = a · (x - 2)²

we will now replace the coordinates of the y-intercept:

- 4 = a · (0 - 2)² = a · 4 ⇒ a = - 4 / 4 = - 1

a = - 1

Finally we get

y = - (x - 2)² = - x² + 4 x - 4

y = - x² + 4 x - 4

God is with you!!!

step-by-step explanation: 2