To shift f(x) to the right three units, we need to replace every x with x-3
f(x) = (x+2)^2 + 1
f(x-3) = (x-3+2)^2 + 1 .... replace x with x-3
f(x-3) = (x-1)^2 + 1
g(x) = (x-1)^2 + 1
The vertex of f(x) is (-2,1). The vertex of g(x) is (1, 1). This is one example showing every point moves three units to the right when going from f(x) to g(x).
