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?

Question

Answered

Verified Answer :

apologiabiology apologiabiology · Answer 1 · 2016-05-20T12:41:07-04:00

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 Link

calculista calculista · Answer 2 · 2018-11-04T19:05:59-05:00

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