https://file.aiquickdraw.com/mathbot/file/1726493395803wz122u50.jpg

The equation provided in the image is \( y = 3|x + 4| \). This is an absolute value function, which has a V-shaped graph.

### Key points for graphing the function \( y = 3|x + 4| \):
1. **Vertex**: The absolute value function has a vertex at the point where \( x + 4 = 0 \), i.e., \( x = -4 \). So, the vertex is \( (-4, 0) \).
2. **Slope**: The coefficient of 3 in front of the absolute value indicates that the slopes of the lines forming the "V" shape are \( 3 \) for the right branch and \( -3 \) for the left branch.
3. **Shape**: The function is symmetric with respect to the vertex, and the graph opens upwards due to the positive coefficient.

### Steps to plot:
- The graph has a vertex at \( (-4, 0) \).
- For values of \( x \geq -4 \), the graph follows the line \( y = 3(x + 4) \).
- For values of \( x < -4 \), the graph follows the line \( y = -3(x + 4) \).

Let me know if you'd like further explanation or if you have any questions!

Here are some related questions:
1. What is the general form of an absolute value equation?
2. How do changes in the coefficient in front of the absolute value affect the graph?
3. How do you find the vertex of an absolute value function?
4. How do you graph piecewise functions like absolute value equations?
5. What role does the slope play in the graph of absolute value functions?

**Tip**: Always identify the vertex of an absolute value function first to understand its symmetry and direction!

Learn how to graph the absolute value function y = 3|x + 4|, including key concepts such as the vertex, slope, and symmetry of the graph. The V-shaped graph has a vertex at (-4, 0), with slopes of 3 and -3 for each branch. Suitable for students in Grades 8-10.

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