Question

Which pair of equations generates graphs with the same vertex?
y = –(x + 4)2 and y = (x – 4)2
y = –4x2 and y = 4x2
y = –x2 – 4 and y = x2 + 4
y = (x – 4)2 and y = x2 + 4

Answer 1

y = –4x² and y = 4x².

Both are of the form a(x−0)²+0, so their vertex is (0, 0). The sign of a changes opening direction but not the vertex.