To reflect the graph of $f(x) = 2x^2$ over the x-axis, we need to multiply the function by $-1$. Reflecting a graph over the x-axis changes the sign of the output values of the function.

So, the equation of the reflected function $g(x)$ would be:

$g(x) = -f(x) = -2x^2$

This means that every point on the graph of $f(x) = 2x^2$ will have its y-coordinate flipped to its negative counterpart.

Would you like further details on graph reflection or any other concept related to this?

Here are 5 related questions to deepen your understanding:

1. How do you reflect a graph over the y-axis?
2. What is the effect of reflecting a graph over the line $y = x$?
3. How does scaling the function vertically or horizontally change the graph?
4. What happens to the graph if you shift $f(x) = 2x^2$ vertically or horizontally?
5. How do the intercepts of the graph change after a reflection over the x-axis?

Tip: Reflecting a graph over the x-axis always changes the sign of the function values without altering the x-values.