Question

The function f(x)=x^2 with vertex (0,0) Is transform to create the function g(x)=f(x-1)-3. What is the vertex of function G.

Answer 1

g(x) = f(x-1) - 3 = (x-1)^2 - 3.

This is the parabola x^2 shifted right 1 and down 3, so the vertex moves from (0,0) to (1,-3).