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The given equation is:

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

This is a quadratic equation in vertex form, which is:

\[
y = a(x - h)^2 + k
\]

where \( (h, k) \) is the vertex of the parabola. In this case:
- \( a = -1 \) (since there is a negative sign in front of the squared term)
- \( h = -3 \) (the opposite of the value inside the parentheses, which is \( +3 \))
- \( k = -4 \) (the constant outside the squared term)

Thus, the vertex of the parabola is:

\[
(-3, -4)
\]

Would you like further details or have any questions?

Here are some related questions to deepen understanding:
1. What effect does the negative sign in front of the squared term have on the graph?
2. How does the value of \( h \) (the horizontal shift) affect the graph of the parabola?
3. What is the role of \( k \) in determining the vertical position of the parabola?
4. How would the graph change if the coefficient \( a \) were positive instead of negative?
5. How can you find the axis of symmetry of this parabola?

**Tip**: The vertex form of a quadratic equation makes it easy to identify the vertex and understand how the graph shifts horizontally and vertically.

Graph the following equations on desmos or on paper. Identify the vertex. y = -(x + 3)^2 - 4

Learn how to graph the quadratic equation y = -(x + 3)^2 - 4 and identify its vertex. This example demonstrates concepts in algebra, focusing on vertex form and quadratic equations. Ideal for students in Grades 8-10.

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