Find g(x), where g(x) is the translation 3 units left of f(x)=x2.

Answer 1

y=f(x) x^2 has vertex at the origin = minimum point of an upward opening parabola

shift 3 units to the left shifts the vertex from (0,0) to (-3,0)

y=(x-h)^2 + k is the general form with vertex = (h,k) = (-3,0)

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

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