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

In the question "Which pair of equations generates graphs with the same vertex?" The correct answer is "y = –4x2 and y = 4x2".
The equation of a parabola with vertex (h, k) is given by (y - k) = 4p(x - h)^2.
By comparison it will be found out that the vertex of the two equations in option B is point (0, 0). i.e. the equations in option B can be rewritten as y - 0 = -4(x - 0)^2 and y - 0 = 4(x - 0)^2.

The answer is option c.