Question

What is the equation of the translated function, g(x), if

f(x) = x2?

g(x) = (x – 4)2 + 6
g(x) = (x + 6)2 – 4
g(x) = (x – 6)2 – 4
g(x) = (x + 4)2 + 6

Answer 1

Option D-
`g(x)=(x+4)^2+6`

Explanation:

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

To find : What is the equation of the translated function, g(x)

Solution :

When we see the attached graph

f(x) vertex point is (0,0)

and g(x) vertex point is (-4,6)

The general form of equation with vertex is
`y=a(x-h)^2+k`

where (h,k) are the vertex.

So, the equation of g(x) form is

`g(x)=(x+4)^2+6`

Therefore, Option D is correct.

Answer 2

we have

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

the vertex is the point
`(0,0)`

The vertex of the function g(x) is
`(-4,6)`

so

the rule of the translation of f(x) to g(x) is equal to

`(x,y)-------> (x-4,y+6)`

that means

the translation is
`4` units to the left and
`6` units up

the equation of g(x) is

`g(x)=(x+4)^(2)+6`

therefore

the answer is

`g(x)=(x+4)^(2)+6`