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

Answer:

Translation: Shift 1 unit left and 5 unit up

Step-by-step 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