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

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

so the vertex is at the point (-1,0)
x^2 has a vertex at (0,0)
So its a translation of 1 unit to the left.

Answer 2

There is a left shift of 1 unit

Explanation:

Given equation is
`f(x)=x^2` and
`g(x)=x^2+2x+1`

the vertex of equation
`f(x)=x^2` is (0,0)

and we see the vertex of
`g(x)=x^2+2x+1` is (-1,0)

we can see this in the graph attached

so, there is translation of vertex of the graph is by left shifting of vertex by 1 unit .