The given problem asks for the expression for $g(x)$, where the function $f(x) = x^2$ is provided.

The graph shows the transformation of the basic function $f(x) = x^2$ into $g(x)$. Based on the graph, we can see that $g(x)$ is a reflection of $f(x) = x^2$ over the x-axis and shifted to the left by 2 units.

This indicates two transformations:

1. A horizontal shift of 2 units to the left: $f(x+2)$.
2. A reflection over the x-axis: $-f(x+2)$.

Thus, the expression for $g(x)$ is:

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

Let me know if you'd like further clarification or additional steps!

Related Questions:

1. What are other types of transformations that can be applied to functions?
2. How do you determine whether a graph is reflected across the x-axis or y-axis?
3. What is the general form of a quadratic function with vertical and horizontal shifts?
4. How would you write the equation for a parabola shifted to the right instead of the left?
5. What are the effects of stretching or compressing a quadratic function?

Tip: Always verify transformations by plugging in key points (like the vertex) and checking how they move on the graph.