How do I show my work as to identify the vertex, axis of symmetry, and x intercepts?

Question

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

Answer 1

g(x) factors very nicely to

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

suppose you write it as

g(x) = (x+1)^2 + 0

and you compare it to
f(x) = a(x-h)^2 + k, which you must have learned and studied to do this topic