https://file.aiquickdraw.com/mathbot/file/17259712361830gva7cqh.jpg

Here is the graph of the parabola \( y = (x + 4)^2 + 3 \):

- The vertex of the parabola is at \((-4, 3)\), marked by the red point.
- The axis of symmetry is the vertical line \(x = -4\), shown as the dashed line.
- The green points \((-3, 4)\) and \((-5, 4)\) are additional points that demonstrate the symmetry of the parabola around its axis.

The graph shows that the parabola opens upward, as expected from the positive coefficient \(a = 1\).

Would you like further details or have any questions?

### Related Questions:
1. How do we determine the width of a parabola?
2. What happens to the graph of a parabola if we change the sign of the coefficient \(a\)?
3. How can we find the x-intercepts of a parabola?
4. What is the effect of the constants \(h\) and \(k\) on the graph of a parabola?
5. How do you graph a parabola if given in standard form?

**Tip:** The vertex form of a quadratic equation makes it easy to identify the vertex and axis of symmetry, which simplifies the process of graphing.

This problem demonstrates how to graph the parabola y = (x + 4)^2 + 3. Learn how to identify the vertex, axis of symmetry, and understand the effect of different parameters in the vertex form of a quadratic equation. Suitable for students in Grades 9-10.

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