Answer
The graph for the equation $y=-\frac{1}{2}{{x}^{2}}$.
Work Step by Step
$y=-\frac{1}{2}{{x}^{2}}$ (equation - 1)
$\begin{align}
& x=-\frac{b}{2a} \\
& =-\frac{\left( 0 \right)}{2\cdot \left( -\frac{1}{2} \right)} \\
& =0
\end{align}$
Now for the y value put $x=0$ in equation (1),
$\begin{align}
& y=-\frac{1}{2}{{\left( 0 \right)}^{2}} \\
& =0
\end{align}$
The vertex is $\left( 0,0 \right)$.
Now choose some value of x on both sides of the vertex and compute the corresponding y value.
$\begin{matrix}
x & y \\
0 & 0 \\
-2 & -2 \\
4 & -8 \\
2 & -2 \\
-4 & -8 \\
\end{matrix}$
