Answer
The graph for the equation $x={{y}^{2}}+3y$.
Work Step by Step
$x={{y}^{2}}+3y$ (equation -1)
$\begin{align}
& y=-\frac{b}{2a} \\
& =-\frac{\left( 3 \right)}{2\cdot \left( 1 \right)} \\
& =-\frac{3}{2}
\end{align}$
Now for the x value put $y=-\frac{3}{2}$ in equation (1),
$\begin{align}
& x=-{{\left( -\frac{3}{2} \right)}^{2}}+3\cdot \left( -\frac{3}{2} \right) \\
& =\frac{9}{4}-\frac{9}{2} \\
& =\frac{9-18}{4} \\
& =-\frac{9}{4}
\end{align}$
The vertex is$\left( -\frac{9}{4},-\frac{3}{2} \right)$.
Now choose some value of x on both sides of the vertex and compute the corresponding y value.
$\begin{matrix}
x & y \\
0 & 0 \\
4 & 1 \\
-2 & -1 \\
-2 & -2 \\
\end{matrix}$
