Answer
$\displaystyle \quad (x-1)^{2}=\frac{1}{2}(y+1)$
Work Step by Step
Opens up. By Table 2,
$\begin{array}{|c|c|c|c|} \hline
{focus}&{directrix}&{equation}& ... opens\\ \hline
{(h,k+a)}&{y=k-a}&{(x-h)^{2}=4a(y-k)}&up\\ \\ \hline \end{array}$
Read from the graph: $\quad (h,k)=(1,-1),$
so the equation has form $\quad (x-1)^{2}=4a(y+1)$
Find $4a$ by using the point on the graph (insert its coordinates into the equation)
$(0-1)^{2}=4a(1+1)$
$1=4a\cdot 2$
$4a=\displaystyle \frac{1}{2}$
The equation is $\displaystyle \quad (x-1)^{2}=\frac{1}{2}(y+1)$
