Question

Which function has a vertex at the origin?

f(x) = (x + 4)2
f(x) = x(x – 4)
f(x) = (x – 4)(x + 4)
f(x) = –x2

Answer 1

f(x) = −x^2.

Reason: y = −x^2 has no horizontal or vertical shifts, so its vertex is at (0,0). The others are shifted: (x+4)^2 → (-4,0), x(x−4)=x^2−4x → (2,−4), (x−4)(x+4)=x^2−16 → (0,−16).