Answer
The graph for the equation $x=-{{y}^{2}}-2y+3$.
Work Step by Step
$x=-{{y}^{2}}-2y+3$ (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),
$\begin{align}
& x=-{{\left( -1 \right)}^{2}}-2\cdot \left( -1 \right)+3 \\
& =-1+2+3 \\
& =4
\end{align}$
The vertex is $\left( 4,-1 \right)$.
Now choose some value of x on both sides of the vertex and compute the corresponding y value.
$\begin{matrix}
x & y \\
1 & 0 \\
3 & 0 \\
0 & -3 \\
-5 & 2 \\
\\
\end{matrix}$
