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? right 1 unit left 1 unit right 2 units left 2 units

 The correct option is (B) left 1 unit.

Step-by-step explanation:  We are given to select the translation that maps the vertex of the graph of the function onto the vertex of the function

We have

We know that the vertex form of a function is given by

where the vertex is the point (h, k).

So, the vertex form of f(x)

where the vertex is (0, 0).

And, the vertex form of g(x) is

where the vertex is (-1, 0).

The required translation from the vertex of f(x) to the vertex of g(x) is

(0, 0)  ⇒  (0-1, 0) = (-1, 0).

Thus, the vertex of f(x) is translated 1 unit left to get the vertex of g(x).

Option (B) is CORRECT.