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

Answer 1

Answer:

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

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