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