Question

Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 + 2x +1?

Answer 1

we know that

The vertex of the function

$f(x)=x^{2}$

is the point $(0,0)$

and

the function

$g(x)=x^{2} +2x+1$

is equal to

$g(x)=(x+1)^{2}$

so

the vertex is the point $(-1,0)$

therefore

the answer is

The translation to maps the vertex of f(x) onto the vertex of g(x) has the following rule

$(x,y)--------> (x-1, y)$

check

$(0,0)----> (0-1,0)----> (-1,0)$ is ok

Answer 2

While the vertex of the function f(x) = x^2 is (0, 0), the vertex of the function g(x) = x^2 + 2x + 1 is (-1, 0).
Whereas both function has same y-cordinate, their x-coordinate are different which indicates that the function g(x) = x^2 + 2x + 1 is a horizontal translation of the function f(x) = x^2.