Question

The quadratic function f(x) = x^2 is transformed to g(x) = -2/3(x+3)^2 + 6 The point (6,36) on the graph of f is transformed to which point on the graph of g?

Could someone please show me how to solve this:\

Answer 1

shift x left 3 (reduce x by three, since g(x+3) = f(x))
scale y by -2/3
shift y up by 6

(3,36*(-2/3)+6) = (3,-24+6) = (3,-18)

check:
g(3) = -2/3 * (3+3)^2 + 6 = -18