The vertex is \((-4, -3)\) because the equation of the parabola is given in vertex form:

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

In the vertex form of a parabola \( y = a(x - h)^2 + k \), \((h, k)\) represents the coordinates of the vertex.

### Breakdown:
- The expression \((x + 4)^2\) can be rewritten as \((x - (-4))^2\), showing that \( h = -4 \). 
- The number \(-3\) is the value of \(k\), which gives the \(y\)-coordinate of the vertex.

So, the vertex of the parabola is at \((h, k) = (-4, -3)\).

The \(-3\) comes from the constant term in the equation, which represents a vertical shift downwards by 3 units from the standard position of the parabola that would otherwise open upwards from the origin.

Would you like more details or have any questions?

### Further Questions:
1. What happens to the vertex if the constant term changes?
2. How does the value of \(h\) affect the position of the vertex?
3. Can we find the vertex if the parabola is not in vertex form?
4. How does the value of \(k\) influence the graph of the parabola?
5. What is the importance of the vertex in the context of parabolas?

### Tip:
The sign of the constants in the vertex form \( y = a(x - h)^2 + k \) directly determines the position of the vertex on the graph, with \(h\) affecting the horizontal position and \(k\) the vertical.

Explore why the vertex of a parabola is located at (-4, -3) through detailed explanations of the vertex form equation (x + 4)^2 - 3. This problem delves into key concepts like vertex form, vertex coordinates, and their significance in parabolic graphs. Suitable for advanced high school students.

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