Parabola Class work
1. A bottlenose dolphin jumps out of the water. The path the dolphin travels can be
modeled by h = -0.2d2 + 2d, where h represents the height of the dolphin and d represents
horizontal distance. What is the maximum height the dolphin reaches?
How far did the dolphin travel before he reentered the water?
2. A boat fires an emergency flare that travels upward at an initial velocity of 25 meters
per second. This can be represented by the function: h = -5t2 + 25t, with representing the
height of the flare in meters and t representing seconds. Use this function to determine
how many seconds it takes the flare to reach a height of 10 meters. Round to the nearest
tenth.
3. To approximate the profit per day for her business, Mrs. Howe uses the formula
p = -x2 + 50x - 350. The profit, p, depends on the number of cases, x, of decorator
napkins that are sold. How many cases of napkins must she sell to break even (p=0)?
4. Jocelyn and Kelly built rockets from assembly kits and are going to launch them at the
same time to see whose rocket flies higher. Jocelyn's rocket's height, in feet, can be
described by the equation y = -16x2 + 180x, while Kelly's is represented by y = -16x2 +
240x
a. Who wins the rocket race? (What is the maximum height each rocket achieves?
b. After how many seconds does each rocket land?
5. A rock is thrown vertically from the ground with a velocity of 24 meters per second.
The path of the rock can be represented by the equation
h = 2 + 24t - 4.9t2. Where h represents the height of the rock and t represents seconds.
a) How many seconds after the rock is thrown will it reach a maximum height, and what
is the maximum height the rock will reach, in meters. Round your answer to the nearest
hundredth.
b) How many seconds after the rock is thrown will it hit the ground? Round your answers
to the nearest hundredth.