Answer:
g(x) = [tex]x^{2}-6x+6[/tex]
Step-by-step explanation:
It is given that f(x) is [tex]x^{2}[/tex].
The graph is basically a parabola opening upward with vertex at origin.If we shift it right by 3 units and down by 3 units, the graph will still be a parabola opening upward but with vertex (3,-3).
The general equation of a parabola opening upward with vertex (a,b) is given by:
y-b = [tex](x-a)^{2}[/tex]
In this case a=3 and b=-3, then we get
y = [tex](x-3)^{2}-3[/tex] = [tex]x^{2}-6x+6[/tex]
Hence g(x) becomes [tex]x^{2}-6x+6[/tex].
