Answer
The equation $x=4-3y-{{y}^{2}}$.
Work Step by Step
$x=4-3y-{{y}^{2}}$ (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).
$\begin{align}
& x=4-3\cdot \left( -\frac{3}{2} \right)-{{\left( -\frac{3}{2} \right)}^{2}} \\
& =4+\frac{9}{2}-\frac{9}{4} \\
& =\frac{4\cdot 4+9\cdot 2-9}{4} \\
& =\frac{16+18-9}{4}
\end{align}$
And,
$x=\frac{25}{4}$
The vertex is$\left( \frac{25}{4},-\frac{3}{2} \right)$.
Now choose some value of x on both sides of the vertex and compute the corresponding y value.
$\begin{matrix}
x & y \\
6 & -1 \\
6 & -2 \\
4 & 0 \\
0 & 1 \\
\end{matrix}$
Now plot all the values of x and y on the rectangular coordinate system and join each point with one another to form a parabola as shown below
