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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).

Which equation best matches the graph shown below?

Explore how to match quadratic equations in vertex form to parabolic graphs. This guide uses a visual example to identify the correct equation, based on vertex, direction, and transformations. Ideal for high school students in Grades 9-12.

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