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 answer: 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!