MIXED QUADRATIC MODELS
Nov 8,9 2012
name _________________________ period
Do the following on a separate piece of paper. Round to the hundredths and show all work.
1.
For a period of 48 months, the average monthly operating cost for a small business C (in dollars) can be approximated by
the model 𝐶 = 0.55𝑡 2 + 550 where t is the number of months. During which month was the average operating cost
$1430?
2.
When an object is dropped, its height h can be determined after t seconds by using the falling object model ℎ = −16𝑡 2 +
𝑠 where s is the initial height. Find the time it takes an object to hit the ground when it is dropped from a height of
a. 160 feet
b. 690 feet
3.
The length of a rectangle is five feet longer than its width. If the area is 84 square feet, find the side lengths.
4. Solve for x if the area of the triangle is 20 square inches using the triangle to the right.
1
𝑥
2
𝑥+2
5. In a track and field event, a contestant had a throw in the shot put that can be modeled by
𝑦 = −0.02𝑥 2 + 𝑥 + 6 where x is the shot put’s horizontal distance and y is the corresponding
height, in feet. How long was the throw?
6. You have a new carpeting installed in a rectangular room. You are charged for 28 square yards of carpet and 60
feet (20 yards) or tack strip. The tack strip is used along the perimeter to secure the carpet in place. Are these
figures correct?
𝑥
10 − 𝑥
7.
2
The equation for an object that is launched or thrown is ℎ = −16𝑡 + 𝑣0 𝑡 + ℎ𝑜 where 𝑣0 𝑎𝑛𝑑 ℎ0 stand for the initial
velocity and initial height, respectively. An object is launched upward with an initial velocity of 64 feet per second from a
platform 80 feet high.
a. Write a height model for the object.
b. How many seconds until the maximum height is reached?
c.What is that maximum height?
d. how many seconds until the object hits the ground?
8. The path of a football kicked from the ground can be modeled by ℎ = −0.02𝑥 2 + 1.2𝑥 where h is the height in yards and x is the
horizontal distance in yards from where the ball is kicked. The crossbar on a field goal post is 10 feet above the ground.
a. write an inequality to find the values of x where the ball is high enough to go over the crossbar.
b. solve the inequality
c. A player attempts to kick a field goal from a distance of 52 yards out. Will the ball have enough height to go over the
crossbar from that distance?
9. A beanbag is thrown through the air from an initial height of 4 meters. From there, the following data points are
collected (time in seconds, vertical height in meters): (0,4) (1,6) (3,4) .
a. Write a quadratic function to model the path of this object
b. How long until the object hits the maximum height?
d.
How long will it be until the object hits the ground?
c. What is that maximum height?
Answers
1. 40th month
2. 3.16 sec, 6.57 sec
3. X=7, 12 feet
4. 8 inches
5. 55.4 feet
6. No, because the area equation 28 = x(10-x) has no real solutions
7. H=-16t^2+64t+80 , 2sec , 144ft , 5 sec
8. a. -0.02x^2+1.2x > 10/3
b. 2.92 < x < 57.08
c. yes (52 is in the solution interval)
9. y = -x^2+3x+4 , 1.5sec , 6.25 ft, 4 sec