Answer:
[tex]g(x)=x^2-6x+6[/tex]
Step-by-step explanation:
Translation of a function
The original function f is
[tex]f(x)=x^2[/tex]
We need to define a second function such as its graph is translated 3 units to the right and 3 units below f(x)
The new function called g(x) must be translated horizontally and vertically. To have it translated to the right, we must replace x by x-3 and to translate the result down, we must subtract 3 as shown
[tex]g(x)=f(x-3)-3[/tex]
[tex]g(x)=(x-3)^2-3[/tex]
[tex]g(x)=x^2-6x+9-3[/tex]
[tex]g(x)=x^2-6x+6[/tex]
Both graphs are shown in the figure below where we can see the translation in both axes
