Answer:
[tex]g(x)=(x-3)^2-6[/tex]
Step-by-step explanation:
we have
The parent function is
[tex]f(x)=x^{2}[/tex] -----> The vertex is the point (0,0)
The function g(x) has a vertex at (3,-6)
so
The rule of the translation of f(x) to g(x) is
(x,y) ------> (x+3, y-6)
That means ----> The translation is 3 units at right and 6 units down
therefore
The equation of the function g(x) is
[tex]g(x)=(x-3)^2-6[/tex]
