Lines, Functions, Systems
Graphing a function of the form $f(x)=a x^{2}$

Graph the function.
\[
g(x)=2 x^{2}
\]

Plot five points on the graph of the function: one point with $x=0$, two points with negative $x$-values, and two points with positive $x$-values. Th graph-a-function button.

Step 1 ：To graph the function \(g(x)=2x^{2}\), we need to plot the points on the graph. We can choose five points: one at \(x=0\), two at negative \(x\) values, and two at positive \(x\) values. We can choose \(x=-2, -1, 0, 1, 2\) for simplicity. We can calculate the corresponding \(y\) values using the function \(g(x)=2x^{2}\). Then we can plot these points on the graph.

Step 2 ：The five points we plotted are \((-2, 8)\), \((-1, 2)\), \((0, 0)\), \((1, 2)\), and \((2, 8)\). These points lie on the graph of the function, confirming that our function and graph are correct.

Step 3 ：\(\boxed{\text{The graph of the function } g(x)=2x^{2} \text{ is a parabola opening upwards.}}\)