Parabola vertex equation

Question

Write an equation of the parabola that has the same shape as the graph of f(x)= 2x², but with (3,2) as the vertex. g(x)=

Answer 1

g(x) = 2(x-3)^2 + 2

a parabola in vertex form is y=a(x-h)^2 + k where (h,k) is the vertex

if (3,2) is the vertex, then h=3 and k=2

g(x) = 2(x-h)^2 +k, substitute 3 for h and 2 for k to get

g(x) =2(x-3)^2 +2

g(x) is the same shape as f(x), but just shifted right by 3 and up by 2