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

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

$g(x)=(x-7)^{2}+5$

Answer 2

Answer:

the answer is B