A point (u,f(u)) becomes (u+h,f(u)+k). Positive h shifts right, while positive k shifts up.
Example
The vertex of f(x)=x2 is (0,0). For g(x)=(x−2)2+3, that vertex moves to (2,3). The original points (1,1) and (−1,1) move to (3,4) and (1,4), preserving symmetry about the new vertical line x=2.
Avoid this mistake
The sign inside looks reversed because the old input 0 now occurs at x=h. Derive the shift from that equation instead of memorizing a slogan.
Mr. Integral