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) = –x^2

Hello,

f(x)=-x²

1)
f(x)=(x+4)²
f'(x)=2(x+4)=0=>x=-4 not 0

2)
f(x)=x²-4x
f'(x)=2x-4=0==>x=2 not 0

3)
f(x)=x²-16
f'(x)=2x=0==>x=0 and y=0²-16=-16 not 0

4)
f(x)=-x²
f'(x)=-2x=0==>x=0 and y=-0²=0 ok