Answer
The graph for the equation $x=-{{y}^{2}}+2y-1$.
Work Step by Step
$x=-{{y}^{2}}+2y-1$ (equation - 1)
$\begin{align}
& y=-\frac{b}{2a} \\
& =-\frac{\left( 2 \right)}{2\cdot \left( -1 \right)} \\
& =1
\end{align}$
Now for the x value put $y=1$ in equation (1),
$\begin{align}
& x=-{{\left( -1 \right)}^{2}}-2\cdot \left( -1 \right)-1 \\
& =-1+2-1 \\
& =0
\end{align}$
The vertex is $\left( 0,1 \right)$.
Now choose some value of x on both sides of the vertex and compute the corresponding y value.
$\begin{matrix}
x & y \\
-4 & 3 \\
-1 & 2 \\
0 & 1 \\
-1 & 0 \\
-4 & -1 \\
\end{matrix}$
