Question 461975
Hi Gina.
This is a quadratic equation given in vertex form.  That makes finding the vertex very easy.
Vertex form of a quadratic equation is:
{{{y=a(x-h)^2+k}}} where the vertex is (h,k)
{{{f(x)=(1/2)*(x+1)^2+1}}} The vertex is (-1,1)
The line of symmetry is the vertical line that goes through the vertex.  Since you already found the vertex, this is very easy. x=-1