Answer
Please see image.
Work Step by Step
The graph of $f(x)=ax^{2}$ is a parabola with $x=0$ as its axis of symmetry.
Its vertex is the origin.
For $a\gt 0$, the parabola opens upward.
For $a\lt 0$, the parabola opens downward.
If $|a|$ is greater than 1, the parabola is narrower than $y=x^{2}.$
If $|a|$ is between $0$ and 1, the parabola is wider than $y=x^{2}.$
The vertex of the graph of $f(x)=a(x-h)^{2}$ is $(h, 0)$ .
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$a=\displaystyle \frac{1}{3}$, opens upward.
The vertex is $(0,0)$.
Make a table of function values and plot the points,
and join with a smooth curve.