https://file.aiquickdraw.com/mathbot/file/1726976756648023tt6j3.jpg

The function provided is:

\[
g(x) = (x + 2)^2
\]

This is a quadratic function and can be rewritten in the form of \( g(x) = (x + h)^2 + k \) where \(h = -2\) and \(k = 0\). The graph of this function is a parabola that opens upwards.

### Key points for graphing:

1. **Vertex**: The vertex of the parabola is at \((-2, 0)\).
2. **Axis of Symmetry**: The line of symmetry for the parabola is \(x = -2\).
3. **Y-intercept**: When \(x = 0\), \(g(0) = (0 + 2)^2 = 4\). Therefore, the y-intercept is \((0, 4)\).
4. **Shape**: Since the coefficient of the squared term is positive, the parabola opens upwards.

### Plotting the graph:
- Start at the vertex \((-2, 0)\).
- Draw the axis of symmetry \(x = -2\).
- Identify another point like \((0, 4)\) and plot it symmetrically on the other side of the axis at \((-4, 4)\).
  
Would you like me to generate the actual graph for you? 

### Additional Questions

1. What is the domain and range of this function?
2. How does the function \(g(x) = (x + 2)^2\) differ from \(f(x) = x^2\)?
3. What happens to the graph if we change the function to \(g(x) = (x + 2)^2 + 3\)?
4. Can you identify any transformations applied to the parent function \(f(x) = x^2\)?
5. How would you describe the concavity of the graph?

**Tip:** For any quadratic function in the form \(y = (x + h)^2 + k\), the vertex will always be at \((-h, k)\).

Graph the following function: g(x) = (x + 2)^2

Learn how to graph the quadratic function g(x) = (x + 2)^2. This includes finding the vertex at (-2, 0), axis of symmetry, and key points such as the y-intercept. This problem is ideal for students in Grades 8-10.

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