Which pair of equations generates graphs with the same vertex?

A) y = - (x + 4) 2 and y = (x - 4) 2

B) y = - 4x2 and y = 4x2

C) y = - x2 - 4 and y = x2 + 4

D) y = (x - 4) 2 and y = x2 + 4

A quadratic equation may be expressed in vertex form as:

y = a (x - h) ² + k, the vertex being (-h, k)

For option A, the vertices are visibly different. (-4, 0) and (4, 0)

For B, the graphs' vertices are the same, (0, 0).

For C, the vertices (can be obtained by differentiating and putting equal to 0) are (0, - 4) and (0, 4)

For D, the vertices are (4, 0) and (0, 4)

Thus, the answer is B.