Question

The graph of f(x) = x2 has been shifted into the form f(x) = (x − h)2 + k: a parabola with a vertex of 3, 3 What is the value of h?

Answer 1

If we write y=f(x)=(x-h)²+k, then y-k=(x-h)². This is vertex form where the vertex is (h,k)=(3,3) so h and k are both 3. We can see this if we put x=3 in the shifted function. This is a minimum point for the function because for every other x f(x) is greater then 3. The minimum point is the vertex.