Which quadratic function in vertex form can be represented by the graph that has the vertex at (-6, 0) and passes through the point (2, 8)?

Question

A. y = -1/8x^2 - 6

B. y = 1/8(x + 6)^2

C. y = 1/8x^2 - 6

D. y = -1/8(x + 6)^2

Answer 1

To find the correct quadratic function in vertex form, we start with the general vertex form of a quadratic function:

y = a(x - h)^2 + k

where (h, k) is the vertex of the parabola.

Given that the vertex is at (-6, 0), we have h = -6 and k = 0.

So now our function is of the form:

y = a(x + 6)^2

Next, we need to determine the value of 'a' by plugging in the point (2, 8) into the function:

8 = a(2 + 6)^2
8 = a(8)^2
8 = 64a
a = 8/64
a = 1/8

Therefore, the correct quadratic function in vertex form is:

y = 1/8(x + 6)^2

This matches option B.