The given graph shows a parabola that opens downwards and is centered at the point (-6, -1), which appears to be the vertex. Based on this, we can identify a few key characteristics of the parabola:

1. The vertex form of a parabola is $y = a(x - h)^2 + k$, where $(h, k)$ is the vertex and $a$ determines the width and direction of the parabola.
   • The vertex is $(-6, -1)$, so $h = -6$ and $k = -1$.
   • The parabola opens downwards, so $a$ must be negative. The value of $a = -4$ based on the given equations.

Now, let's match the equation to the graph:

• Since the vertex is $(-6, -1)$, we expect $h = -6$ and $k = -1$.
• The equation must be in the form $y = -4(x + 6)^2 - 1$.

Thus, the correct answer is: $\boxed{y = -4(x + 6)^2 - 1}$

Would you like further clarification or details on this problem?

Here are 5 related questions to expand on this:

1. How do you derive the equation of a parabola from a graph?
2. What role does the value of "a" play in determining the shape of the parabola?
3. How do you identify the vertex from a given quadratic equation?
4. How can you find the axis of symmetry for a parabola?
5. How does changing the value of "k" affect the graph of a parabola?

Tip: Remember that the sign of "a" in the vertex form indicates whether the parabola opens upwards (positive) or downwards (negative).