Question

The vertex form of a function is g(x) = (x – 3)2 + 9. How does the graph of g(x) compare to the graph of the function f(x) = x2?

Answer 1

we have

$g(x)=(x-3)^{2}+9$

This is the equation of a vertical parabola with vertex at point $(3,9)$

The parabola open upward------> the vertex is a minimum

$f(x)=x^{2}$

This is the equation of a vertical parabola with vertex at point $(0,0)$

The parabola open upward------> the vertex is a minimum

so

the rule of the translation is

$f(x)------> g(x)$

$(x,y)-----> (x+3,y+9)$

that means

the translation is $3$ units to the right and $9$ units up

the graph of the function g(x) is the translated graphic of the function f(x) $3$ units to the right and $9$ units up

therefore

the answer is

g(x) is shifted $3$ units right and  $9$  units up

Answer 2

In y=a(x-h)^2+k
vertex=(h,k)

f(x)=x^2,
 the vertex is (0,0)
it opens up

g(x)=(x-3)^2+9
vertex is (3,9)
opens up