The equation you've provided is in vertex form of a quadratic function:

$y = -4(x + 5)^2 + 4$

This form is generally written as:

$y = a(x - h)^2 + k$

where $(h, k)$ is the vertex of the parabola, and $a$ determines the direction and width of the parabola.

Let's break down the components:

1. Vertex:

   • The vertex is $(-5, 4)$, which comes from the values $h = -5$ and $k = 4$ (the signs are opposite inside the parentheses).

2. Direction of the parabola:

   • Since $a = -4$ (a negative number), the parabola opens downward.

3. Stretch/Compression:

   • The absolute value of $a$ (which is 4) tells us that the parabola is narrower than a regular parabola. A larger value of $|a|$ makes the parabola steeper.

Would you like a more detailed explanation of the parabola's characteristics, or would you like help solving a related problem?

Here are five related questions:

1. How do you find the axis of symmetry for this quadratic function?
2. What is the equation of the directrix of this parabola?
3. How would you graph this quadratic equation step-by-step?
4. What is the range of the function $y = -4(x + 5)^2 + 4$?
5. How do you find the x-intercepts (if any) of this parabola?

Tip: The vertex form makes it easier to identify the vertex directly, which is especially useful for graphing quadratics.