Math III - wsfcs.k12.nc.us
Math II Name_________________________
Unit 3: Quadratic Applications Date_______________Period_____
1. Miranda throws a set of keys up to her brother, who is standing on a third-story balcony with his hands 38 feet above the ground. If Miranda throws the key with an initial velocity of 40 feet per second, the equation h = -16t2 + 40t + 5 gives the height h of the keys after t seconds.
a) How long does it take the keys to reach their highest point? ___________
b) How high do the keys reach? _________
c) Will her brother be able to catch the keys, why or why not?
2. A stone was thrown from the top of a cliff 60 meters above sea level. The height H meters, of the stone above sea level t seconds after it was released is given by [pic].
a) Find the time taken for the stone to reach its maximum height. ___________
b) What is the maximum height above sea level reached by the stone? __________
c) How long is it before the stone strikes the water? _________
3. The height H metres of a cannonball t seconds after it is fired into the air is given by [pic]
a) Find the time taken for the cannonball to reach its maximum height. _________
b) What is the maximum height reached by the cannonball? __________
c) How long does it take for the cannonball to fall back to earth? _____________
4. The height of a punted football can be modeled with the quadratic function [pic]
The horizontal distance in feet form the point of impact with the kicker’s foot is x, and h is the height of the ball in feet.
a) What is the maximum height of the punt? _______________
b) The nearest defensive play is 5 ft horizontally from the point of impact. How high must the player reach to block the punt? ________________
c) Suppose the ball was not blocked but continued on its path. How far down the field would the ball go before it hit the ground? _____________
5. Randall Curtain High School’s changing enrollment, E, for 1955 to 1975 can be modeled by the
Equation, [pic]. (Round each answer to the nearest whole number.)
a) If 1950 is represented by t = 0, in what year was the enrollment at a minimum?____________
b) What was the minimum enrollment?______________________
6. In 1970, Harris Teeter opened a grocery store in your neighborhood. For the next twenty years, annual
sales, S (in millions of dollars), can be modeled by the equation [pic] where
t = 0 represents 1970.
a) During which year did they make the most money?__________________________
b) What was the maximum in annual sales?
7. The function [pic] describes newspaper circulation (in millions) in the
United States for the years 1920 to 1998 (x = 20 for 1920). Identify periods of increasing and
decreasing circulation.
a) According to the function, when did newspaper circulation peak?___________________
b) When will circulation reach 45 million?__________________________
8. The base of a triangle is 3 cm longer than its altitude. The area of the triangle is 35 cm2. Find the
altitude.
9. The length of a rug is twice its width. Its area is 12.5 sq. meters. Find the dimensions of the rug.
10. A rectangular painting measures 3 m by 5 m. A frame of uniform width is put around the painting. If the painting and the frame together cover an area of 39 m2, how wide is the frame?
11. A rectangular pond measures 5 m by 7 m. A stone walk of uniform width is built around the pond.
If the walk and the pond together cover an area of 59 m2, how wide is the walk?
12. Suppose that 60 meters of fencing is available to enclose a rectangular garden, one side of which will
be against the side of a house. What dimensions of the garden will guarantee a maximum area?
13. The length of a rectangular road sign is 1 m less than twice the width. The area is 28 m2. Find the dimensions of the road sign.
14. The following data represents the average maximum and minimum temperatures recorded each month in Raleigh, NC, over a 6-month period. The temperatures recorded are in degrees Fahrenheit.
|Max |72.3 |79.0 |85.2 |88.2 |87.1 |81.6 |
|Min |46.5 |55.3 |62.6 |67.1 |68.0 |60.4 |
(A) Find the QUADRATIC equation that best models the data.
B) Predict minimum temperature if the maximum temperature is 90.
(C) Predict the maximum temperature if the minimum temperature is 40.
15. The table compares the weight and wing area of several types of birds.
|Weight (g) |25 |47 |78 |93 |143 |
|Wing Area (cm2) |87 |186 |245 |190 |357 |
(A) Find the [pic]values for the linear and quadratic regressions of this data.
(B) Determine if the data is linear or quadratic. Why?
(C) Write the equation that best models the data.
(D) Predict the wing area of a bird that weighs 60 ounces.
(E) Predict the weight of a bird with a wing area of 500 cm2
16. The table below shows the study time and test scores for a number of students.
|Study Time (min.) |7 |14 |17 |23 |27 |33 |
|Height (ft) |250 |243 |225 |205 |175 |120 |
(A) Find the [pic]values for the linear and quadratic regressions of this data.
(B) Determine if the data is linear or quadratic. Why?
(C) Write the equation that best models the data.
(D) Predict his distance from the ground after 3.5 seconds.
(E) Predict when he will be at a height of 150 ft.
(F) Predict when he will hit the ground.
18. This data table shows the per capita consumption of broccoli, b (in pounds) for the years 1980 through 1989. Let t represent the year, with t = 0 corresponding to 1980.
Year |1980 |1981 |1982 |1983 |1984 |1985 |1986 |1987 |1988 |1989 | |Pounds |1.6 |1.8 |2.2 |2.3 |2.7 |2.9 |3.5 |3.6 |4.2 |4.5 | |
(A) Find the [pic]values for the linear and quadratic regressions of this data.
(B) Determine if the data is linear or quadratic. Why?
(C) Write the equation that best models the data.
(D) In which year was the per capita consumption of broccoli 5 pounds?
(E) What would the per capita consumption of broccoli be in 2005?
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