Question

Which quadratic function in vertex form has a vertex at (-2, 6) and passes through the point (-4, 8)?

A. y = 1/2 ( x - 2 ) ^2 + 6

B. y = -1/2 ( x - 2 ) ^2 - 6

C. y = -1/2 ( x - 2 ) ^2 + 6

D. y = 1/2 ( x + 2 ) ^2 + 6

Answer 1

y = -1/2(x + 4)² + 2 or y = -1/2x²- 4x - 6

Explanation:

Given

Vertex = (-4, 2)

The graph passes through the point (-8, -6)

The function in vertex form is:

y = a(x + 4)² + 2

Substitute the coordinates of (-8, -6) and find the value of a:

-6 = a(-8 + 4)² + 2

-8 = 16a

a = -1/2

The function is:

y = -1/2(x + 4)² + 2

or in standard form:

y = -1/2(x² + 8x + 16) + 2 = -1/2x²- 4x - 6

Answer 2

D this is because (-2,6) is the vertex and the x-variable in the vertex is always positive and the y-variable stays the same so the answer is D