1. Hot Air Balloon Investigation Retrieved from Tina Franzen (MCC9-12.F.IF.7; MCC9-12.F.IF.7c)

2. Ginger and Paul want to ride in a hot air balloon. Their trip can be described by the following function: h(t) = -1.252t 4 + 10.732t 3 – 30.377t 2 +29.931t where the height, h meters, of the balloon is relative to the ground for t hours.

3. Change the WINDOW Settings Since time is along the x-axis, and we do not have a negative time, set X MIN = 0. The ride will not take more than 5 hours so set X MAX = 5. Since the height of the balloon is relative to the ground, we will not go below the ground level. Set Y MIN = 0.

4. Graph it! Press the Y = button & type in the following equation: -1.252x^4+10.732x^3-30.377x^2+29.931x Press the GRAPH button.

5. What Does the Graph Show Us? 1. The graph starts off at the origin. Why? 2. Describe what is happening on the trip from the beginning to the end.

6. What Does the Graph Show Us? 3. What is the maximum height that the hot air balloon reached? 4. When did the balloon reach its maximum height?

7. What Does the Graph Show Us? 5. How long did the trip last? How do you know? 6. What type of function would best describe this graph?