Solution:

This problem involves analyzing a graph to complete the sentences. Based on the given details:

1. Type of Function: The function represents a quadratic function because the graph forms a parabolic shape, opening downward.

2. Michael Jordan's Hang Time: Hang time is the total time he remains airborne. Based on the graph, the height starts at $t = 0$, returns to the ground at $t = 0.9$, and thus the hang time is 0.9 seconds.

3. Maximum Height: The graph reaches its maximum height at $t = 0.3$ or $t = 0.6$ (the vertex). At this point, the height is $h = 0.9$ meters. Thus, the maximum height is approximately 0.9 meters.

4. Height Between $t = 0.5$ and $t = 1$: For $t$ in the interval $[0.5, 1]$, the function is decreasing.

   • At $t = 0.5$, $h = 0.8$ meters.
   • At $t = 0.6$, $h = 0.9$ meters.
   • At $t = 0.7$, $h = 0.7$ meters.
   • At $t = 0.9$, $h = 0$ meters.

Thus, for $t$ between $0.5$ and $1$, the height ranges from 0.9 meters to 0 meters, decreasing.

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Completed Sentences:

1. This is the graph of a quadratic function.
2. Michael Jordan's hang time is 0.9 seconds.
3. The maximum height is about 0.9 meters.
4. For $t$ between $t = 0.5$ and $t = 1$, the height is decreasing from 0.9 meters to 0 meters.

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Would you like a breakdown of any specific part of this explanation?
Here are 5 related questions to explore further:

1. How do you determine if a function is quadratic from its graph?
2. Why is the hang time calculated as the time from takeoff to landing?
3. What is the significance of the vertex in a quadratic function?
4. How do you compute the height of a parabola at specific intervals?
5. What are some practical applications of analyzing projectile motion using quadratic functions?

Tip: Always identify key points on the graph (such as vertex, intercepts, and symmetry) to understand the behavior of quadratic functions.