Analyzing the Data: Suppose that the path of the first model rocket follows the equation

h(t)= -6 * (t - 3.7)^2 + 82.14,

Where t is the time in seconds (after the first rocket is launched), and h(t) is the height of each rocket, in feet.

3. Compare the equation with the graph of the function. Assume this graph is a transformation from f(t)= -6t^2. What does the term -3.7 do to the rocket’s graph? What does the value t= 3.7 represent in the science project? (What happens to the rocket?)

4. Again assuming a transformation from f(t)= -6t^2, what does the term 82.14 do to the rocket’s graph? What does the value h(t)= 82.14 represent in the science project? (What is happening to the rocket?)

5. Serena and Jack launch the second rocket 3 seconds after the first one. How is the graph of the second rocket different from the graph of the first rocket? Describe in terms of the vertical and horizontal shift.

6. What is the equation of the second rocket?

7. They launch the third rocket 3 seconds after the second rocket and from a 20-foot-tall platform. What will the graph of the third rocket look like? Describe in terms of vertical and horizontal shift.

8. What is the equation of the third rocket?