1. Ramona and James each build a rocket launcher. They launch a model rocket using Ramona's launcher, and on its way back down, it lands on the roof of a building that is 320 feet tall. The height of the rocket can be represented by the equation H,(x) = -16x² + 200x, where x represents the time in seconds and H,(x) represents the height. Ramona and James take the stairs to the roof of the building and relaunch the rocket using James's rocket launcher. The rocket lands back on the ground. The height of the rocket after this launch can be represented by the equation H₂(x) = -16x² + 192x + 320.

Question

1. Ramona and James each build a rocket launcher. They launch a model rocket using Ramona's launcher, and on its way back down, it lands on the roof of a building that is 320 feet tall. The height of the rocket can be represented by the equation H,(x) = -16x² + 200x, where x represents the time in seconds and H,(x) represents the height. Ramona and James take the stairs to the roof of the building and relaunch the rocket using James's rocket launcher. The rocket lands back on the ground. The height of the rocket after this launch can be represented by the equation H₂(x) = -16x² + 192x + 320.

b. Use technology to sketch a graph of the functions.
c. Does it make sense in terms of the problem situation to graph the functions outside of Quadrant l? Explain your reasoning.
d. Explain why the graphs of these functions do not intersect.
e. Ramona believes that she can add the two functions to determine the total height of the rocket at any given time. Write a function S(x) that represents the sum of H¹(x) and H²(x). Show your work.

Answer 1

of course the graphs intersect at x=40:

-16x² + 200x = -16x² + 192x + 320
8x = 320
x = 40