The given function is:

\[
f(x) = -3(x - 2)^2 - 4
\]

This represents a quadratic function in vertex form, \( f(x) = a(x - h)^2 + k \), where:
- \( a = -3 \),
- \( h = 2 \), and
- \( k = -4 \).

### Key characteristics of this function:
1. **Vertex**: The vertex of the parabola is at \( (h, k) = (2, -4) \).
2. **Direction**: Since \( a = -3 \) (negative), the parabola opens **downward**.
3. **Stretch**: The factor of \( -3 \) means the parabola is vertically stretched by a factor of 3 compared to the standard parabola \( y = (x-h)^2 \), making it narrower.
4. **Axis of symmetry**: The axis of symmetry is the vertical line \( x = 2 \).
5. **Maximum value**: The function reaches its maximum value at the vertex, which is \( -4 \).

Would you like a detailed graph or further breakdown of the function?

Here are five related questions to consider:
1. What is the domain and range of this quadratic function?
2. How would you find the \(x\)-intercepts of this function?
3. How do you determine whether the function has a maximum or minimum value?
4. What would happen to the graph if the value of \(a\) was positive instead of negative?
5. How does the vertex form compare to the standard form of a quadratic function?

**Tip**: The vertex form of a quadratic function is useful for identifying the vertex and the direction of the parabola easily without completing the square.

Explore the quadratic function f(x) = -3(x - 2)^2 - 4, including key concepts such as vertex form, axis of symmetry, and maxima of the function. Suitable for high school students in Grades 9-12.

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