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.
$\begin{matrix}
x & y \\
5 & 1 \\
-1 & -2 \\
5 & -3 \\
-3 & -1 \\
\\
\end{matrix}$
