Question

Which translation maps the graph of the function f(x) = x2 onto the function g(x) = x2 + 2x + 6?

Answer 1

The graph went left 1 and up 6. You could complete the square to find out or just graph it!
Hope this helps!

Answer 2

Translation: Shift 1 unit left and 5 unit up

Explanation:

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

Translation function,
`g(x)=x^2+2x+6`

First we change g(x) into vertex form and then check the translation.

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

Completing square

`g(x)=(x^2+2x+1)+5`

`g(x)=(x+1)^2+5`
`\because a^2+2ab+b^2=(a+b)^2`

Now, we will compare the function with f(x)

`f(x)=x^2`

Shift f(x) 1 unit left

`f(x)=(x+1)^2`

Shift f(x) 5 unit up

`f(x)=(x+1)^2+5=g(x)`

Translation: 1 unit left and 5 unit up