Solving Problems Involving Quadratic Relations

Solve the following problems involving quadratic relations. You can choose to do so algebraically or graphically. If you choose to solve it graphically, you must attach a rough sketch of the graph from Desmos. If you choose to solve algebraically, SHOW ALL OF YOUR WORK.

1. A model rocket is launched from a platform. The trajectory of the rocket can be modelled by the relation  , where h is the height of the model rocket in meters and t is the time in seconds.
a) What is the height of the platform?
b) What is the height of the model rocket after 4 seconds?
c) What is the maximum height reached by the rocket? How long does it take to reach this height?
d) Approximately how long is the rocket in the air? 

A toy rocket is shot vertically into the air from a 80-foot platform. The height, h(t) in feet, of the rocket above the ground after t seconds is modeled by h(t) = -16t^2 + 128t + 80. (Give solutions accurate to two decimal places. No credit will be awarded for a calculator-only solution.) (a) How high is the rocket after 3 seconds? (b) How many seconds will it take the rocket to reach its maximum height? (c) What is the maximum height of the rocket? (d) How long will it take the rocket to reach the ground?

MAFS.912.F-IF.3.8 The engineers at Estes Rockets are trying to improve its best selling model rocket for a faster launch speed an higher maximum altitude. The height of the rocket can be calculated by the equation h(t)16t12 where h represents height in feet and t represents time in seconds. a. Rewrite the height function so that the engineers can identify the maximum height easily. What is the maximum height of the new model? How long will it take for the rocket to reach this height? How long will the rocket be in the air? When the rocket reaches 60 feet on the descent, a parachute is released to cushion the fall. When will the b. c. parachute be released? d. The height of the old model can be calculated using the equation h(c)-14t2 +112t. Represent this function in a different form than in part a. Is the new model indeed an improvement on height and launch speed? Why or why not? Use mathematics to support your answer.

A model rocket is launched with an initial upward velocity of 235 ft/s. The rocket's height h (in feet) after t seconds is given by the following. h = 253 t - 16 t2 Find all values of t for the which the rocket's height is 151 feet. Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)