Here is the graph of the function $f(x) = -2(x+3)^2$. The graph is a downward-facing parabola, as indicated by the negative coefficient in front of the squared term. The vertex of the parabola is at $(-3, 0)$, and it opens downward due to the negative sign.

Would you like further details or have any questions about this graph?

Here are some related questions you might find interesting:

1. How does changing the coefficient affect the width of the parabola?
2. What happens if we shift the function horizontally or vertically?
3. How does the value of $f(x)$ change as $x$ moves further from the vertex?
4. What is the domain and range of this function?
5. How would this graph change if the function were $f(x) = 2(x + 3)^2$?

Tip: The coefficient of the squared term in a parabola controls whether it opens upwards (positive) or downwards (negative) and affects its steepness.