Answer
$(x-1)^2=\frac{1}{2}(y+1)$
Work Step by Step
1. Use the given graph, the parabola opens up with vertex $(1,-1)$, thus we have $(x-1)^2=4p(y+1)$
2. Use the point $(0,1)$ on the curve, we have $(0-1)^2=4p(1+1)$, thus $p=\frac{1}{8}$
3. The equation is $(x-1)^2=\frac{1}{2}(y+1)$
