The question asks to graph the function $f(x) = x^2 - 2$ and describe how it was translated from the function $f(x) = x^2$.

Translation description:

The base function is $f(x) = x^2$, which is a standard parabola with its vertex at the origin (0, 0). The function $f(x) = x^2 - 2$ can be seen as a vertical translation of $f(x) = x^2$. The "-2" means the graph is shifted downward by 2 units. Therefore, the vertex of the parabola moves from (0, 0) to (0, -2).

In summary:

• Vertical Translation: The graph is shifted 2 units downward.

Would you like further details or help with graphing it? Here are five questions to expand on this topic:

1. How do horizontal translations affect the graph of a quadratic function?
2. What happens to the graph of $f(x) = x^2$ when a coefficient is added to $x^2$ (e.g., $f(x) = 2x^2$)?
3. How does the graph change if the function were $f(x) = (x - 2)^2$?
4. Can you explain how to determine the vertex of a quadratic function?
5. What effect does a negative sign before the $x^2$ term have on the shape of the parabola?

Tip: When graphing quadratic functions, always start by identifying the vertex and direction of the parabola (whether it opens up or down).