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. 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. 1. compare the equation with the graph of the function. assume this graph is a transformation from f(t) = –6t2. 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? ) 2. 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? ) 3. 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. 4. what is the equation of the second rocket? 5. 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. 6. what is the equation of the third rocket? 7. answer the following questions about the three rockets. refer to the graph of rocket heights and times shown above. 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?