What is the vertex of the function g(x) = (x  - h)²?

The correct answer is: (h, 0)

The vertex of the graph  is .
The parent function was f(x)=x2 whose vertex is (0,0)
f(x)=(x-h)2 is identical to the parent function, except for the +h which is the x-intercept.
x-h=0 x=h
So each coordinate, and therefore the whole graph is shifted h units to the right. So, the coordinates of vertex becomes (h,0)
So, the new vertex is (h,0)