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.

Explore the graph of the quadratic function f(x) = -2(x+3)^2. This problem covers key algebraic concepts like vertex form, transformations, and the effect of negative coefficients on parabolas. Suitable for students in Grades 9-11, with a step-by-step breakdown of graphing the parabola.

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