Solving Quadratic Applications Homework (2.1)
PC
Name:
LB
Date:
1.
The height of an object thrown upward from the roof of a building 408 ft tall, with an initial
velocity of 96 ft/sec, is given by the equation h = −16t 2 + 96t + 408 , where h represents the
height of the object after t seconds. How long will it take the object to hit the ground?
Answer in exact form and decimal form rounded to the nearest hundredth.
2.
The cost to produce bottled spring water is given by the cost equation: C = 16x + 63 , where x
is the number of bottles in thousands. The total revenue from the sale of these bottles is
given by the equation: R = −x 2 + 326x − 18,463 .
3.
a.
Determine the profit equation (profit = revenue – cost).
b.
After a bad flood contaminates the drinking water of a nearby community, the owners
decide to bottle and donate as many bottles of water as they can, without taking a loss
(i.e., they break even: profit or P = 0). Approximately how many bottles will they
produce for the flood victims?
The revenue for a manufacturer of microwave ovens is given by the equation R = x ( 40 − 13 x ) ,
where revenue is in thousands of dollars and x thousand ovens are manufactured and sold.
What is the minimum number of microwave ovens that must be sold to bring in a revenue of
at least $900,000?
4.
For the years 1995 to 2002, the number N of cellular phone subscribers (in millions) can be
modeled by the equation N = 17.4x 2 + 36.1x + 83.3 , where x = 0 represents the year 1995
[Source: Data from the 2005 Statistical Abstract of the United States, Table 1372, page 870]. If
this trend continued, in what year did the number of subscribers reach or surpass 3750
million?
5.
The Sandusky Little League uses a baseball throwing machine to help train 10-year-old
players to catch high pop-ups. It throws the baseball straight up with an initial velocity of 48
ft/sec from a height of 3.5 ft.
a. Find an equation that models the height of the ball t seconds after it is thrown.
s (t ) = −16t 2 + v 0t + s 0
b. What is the maximum height the baseball will reach? How many seconds will it take to
reach that height?
6.
As a promotion for the Houston Astros downtown ballpark, a competition is held to see who
can throw a baseball the highest from the front row of the upper deck of seats, 83 ft above
field level. The winner throws the ball with an initial vertical velocity of 92 ft/sec and it lands
on the infield grass.
a. Find the maximum height of the baseball.
b. How much time is the ball in the air?
Extra Credit: In her first project after being employed by Land Scapes International, Becky designs a
decorative water fountain that will shoot water to a maximum height of 48 ft. What should
be the initial velocity of each drop of water achieve this maximum height? (Hint: Use a
graphing calculator and a guess-and-check strategy.)