A quadratic function y=f(x)y=f(x) is plotted on a graph and the vertex of the resulting parabola is (3, -3)(3,−3). What is the vertex of the function defined as g(x)=-f(x-3)g(x)=−f(x−3)?

Answer 1

g(x) vertex = (6,3)

f(x) = (x-3)^2 -3 is an upward opening parabola with vertex (3,-3)

g(x) = -f(x-3) = -[(x-3-3)^2 -3] = -(x-6)^2 +3 is a downward opening parabola with vertex (6,3)

replace x with x-3 in f(x) and change the sign