what is the function rule for the problem below?

Question

the function f(x) = x squared. The graph of g(x) is f(x) translated to the left 5 units & down 3 units. What is the function rule for g(x)?

Answer 1

f(x) is a parabola with vertex at the origin (0,0).

The vertex of g(x) has to be at (-5,-3) because the 5 units to the left means 0-5=-5 (x coord); and 3 units down means 0-3=-3 (y coord).

Therefore g(x)=(x+5)²-3 (when x=-5, y=-3 which puts the vertex at (-5,-3)).