Answer
True
Work Step by Step
$f\left( x \right)=a{{x}^{2}}$
The function is of second degree and gives the graph of a parabola.
Let $a=1$ and take the value of x and make a table of values,
$\begin{matrix}
x & f\left( x \right)=1\cdot {{x}^{2}} \\
-2 & 4 \\
-1 & 1 \\
0 & 0 \\
1 & 1 \\
2 & 4 \\
\end{matrix}$
The graph for the table is shown below.
So, the graph is a parabola with vertex at $\left( 0,0 \right)$ and has $x=0$ as an axis of symmetry as the graph is symmetrical with respect to the $x=0$ axis.
Now, for the function $f\left( x \right)=a{{x}^{2}}$, if $a<0$, then the parabola opens downward, and if $a>0$, then parabola opens downward.
Therefore, upon comparing the given function $g\left( x \right)=5{{x}^{2}}$ with the standard format function of a parabola $f\left( x \right)=a{{x}^{2}}$, it is concluded that given function is of parabola with vertex at $\left( 0,0 \right)$ and having symmetry with respect to $x=0$.
