Answer
Graph $B$
Work Step by Step
The function in the form $y=a(x-h)^2+k$ has a vertex at $(h,k)$.
Given: $$y=2(x+1)^2-3.$$ Rewrite: $$y=2(x-(-1))^2+(-3).$$ It follows that $a=2$, $h=-1$, $k=-3$. The vertex is $$(h,k)=(-1,-3)$$ and the parabola opens up since $a>0$.
The graph which fits is graph $B$.