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

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

Answer 2

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