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.