The graph of g(x) is a translation of the function f(x) = x2. the vertex of g(x) is located 5 units above and 7 units to the right of the vertex of f(x). which equation represents g(x)?
g(x) = (x + 7)2 + 5
g(x) = (x – 7)2 + 5
g(x) = (x + 5)2 + 7
g(x) = (x – 5)2 + 7

we know that

The graph of g(x) is a translation of the function f(x)

so

the vertex of f(x) is the point

the vertex of g(x) is located units above and units to the right of the vertex of f(x)

The rule of the translation is

Find the vertex of the function g(x)

the vertex of g(x) is the point

the equation of the function g(x) in the vertex form is equal to

where

(h,k) is the vertex

substitute the value of the vertex in the equation

the answer is

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)