https://file.aiquickdraw.com/mathbot/file/172693427324563w4evbs.jpg

https://file.aiquickdraw.com/mathbot/file/17269343120326p7s18r6.jpg

Based on the images you uploaded, the task is to match the given graphs with the appropriate functions. Let's go through the graphs and functions:

1. **Graph 1** (Left image):
   - This is an upside-down parabola, indicating a quadratic function with a negative leading coefficient. The vertex appears to be above the x-axis, suggesting a vertical shift upwards.
   - The function that best matches this is \( y = -x^2 + 5 \), which is a downward-facing parabola with its vertex at \( (0, 5) \).

2. **Graph 2** (Right image):
   - This is a V-shaped graph, typical of an absolute value function. The graph appears to be inverted and vertically shifted up by 4 units.
   - The function that matches this is \( y = -|x| + 4 \), which describes an inverted absolute value graph with a vertical shift of 4 units upwards.

### Matching:
- **Graph 1** matches \( y = -x^2 + 5 \).
- **Graph 2** matches \( y = -|x| + 4 \).

Would you like further details or clarification on these solutions? 

Here are some additional questions related to this topic:
1. What is the general form of a quadratic function and how does it affect the graph?
2. How do transformations like vertical shifts and reflections affect the graph of an absolute value function?
3. Can a parabola open sideways, and what kind of equation represents such a graph?
4. How does the leading coefficient in a quadratic function affect the width of the parabola?
5. What is the difference between the graph of \( y = |x| \) and \( y = -|x| \)?

**Tip:** Understanding the effect of transformations (translations, reflections, stretching) on basic graphs like parabolas and absolute value functions will help you quickly identify graph types!

Learn how to match graphs with quadratic and absolute value functions. This example covers transformations including vertical shifts, reflections, and translations, suitable for students in grades 9-12.

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