Question 1064461
Lead coefficient is 1,  a positive value, so the vertex will be the minimum value for f(x).


{{{f(x)=x^2+2x+c}}}
{{{f(x)=x^2+2x+1+c-1}}}
{{{(x+1)^2+c-1}}}


Vertex point would be  (-1,c-1).


If you want {{{f(-1)=sqrt(2)}}} for the minimum function value, then
{{{c-1=sqrt(2)}}}
{{{highlight(c=1+sqrt(2))}}}