We are given two functions:

• $f(x) = x^2$
• $g(x) = (x - 2)^2 - 4$

The transformation from $f(x)$ to $g(x)$ involves two shifts:

1. Horizontal shift: The expression $(x - 2)$ indicates a shift to the right by 2 units.
2. Vertical shift: The constant term $-4$ outside the squared term indicates a shift downward by 4 units.

Thus, the graph of $g(x)$ is a translation of the graph of $f(x) = x^2$ 2 units to the right and 4 units downward.

Now, for the missing terms in the statement:

"The graph of $g$ is a translation 2 units to the right and 4 units down of the graph of $f$."

Do you need further explanation or clarification?

Here are 5 questions to deepen your understanding:

1. What is the general form of a quadratic transformation?
2. How would the graph change if the transformation were $g(x) = (x + 2)^2 - 4$?
3. Can you identify other transformations that affect the shape of the graph, like stretching or reflection?
4. How do translations impact the vertex of a parabola?
5. What are the key features (vertex, axis of symmetry) of the graph of $g(x)$?

Tip: When identifying transformations, always look for horizontal and vertical shifts, stretches, and reflections by examining the equation's structure.