(30 points!) 4.3.4 Journal: Shifting Functions The Students' Conjectures: Serena and Jack are launching three identical model rockets, each at a different time. Jack says that they need to recalculate the graph each time, but Serena thinks they can just shift the function of the first graph.

1. (I can do this one myself)

2. Do you agree with Serena that you can draw the graphs for the other two rockets by shifting the functions? Or do you think that Jack is correct that you need to recalculate the other two? Explain.

3. (Check out the attachment below to see the graph and everything) Compare the equation with the graph of the function. Assume this graph is a transformation from the f(t) = -6t². What does the term of -3.7 do the rocket's graph? What does the value of t=3.7 represent in the science project? (What happens to the rocket?)

4. Again assuming a transformation from f(t) = -6t², 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 the vertical and horizontal shift.

8. What is the equation of the third rocket?

9. Answer the following questions about the three rockets. Refer to the graph of rocket heights and times shown below. (Second attachment below)
(a) Approximately when is the third rocket launched?
(b) Approximately when does the first rocket land?
(c) What is the approximate interval during which all three rockets are in the air?

Thank you so much for your help!!