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)?
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
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.