Question

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

Answer 1

the answer is B

Answer 2

we know that

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

so

`f(x)=x^(2)`

the vertex of f(x) is the point
`(0,0)`

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

The rule of the translation is

`(x,y)--------> (x+7,y+5)`

Find the vertex of the function g(x)

`(0+7,0+5)=(7,5)`

the vertex of g(x) is the point
`(7,5)`

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

`g(x)=(x-h)^(2) +k`

where

(h,k) is the vertex

substitute the value of the vertex in the equation

`g(x)=(x-7)^(2) +5`

the answer is

`g(x)=(x-7)^(2)+5`