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!