Name Quadratic Application Problems 1. A roof shingle is dropped from a rooftop that is 100 feet above the ground. The height y (in feet) of the dropped roof shingle is given by the function y = -16t 2 + 100 where t is the time (in seconds) since the shingle is dropped. i. Use your equation to find the height of the shingle after 2 seconds. ii. Use your graph to find the time at which the shingle is 10 feet above the ground. (Hint: Draw a horizontal line at y = 10, then find where it intersects the graph of the shingle s height.) 2. The cables between the two towers of the Takoma Narrows Bridge form a parabola that can be modeled by the graph of the equation y = 0.00014x 2 0.4x + 507 where x and y are measured in feet. (See the picture of a similar bridge on page 637 of your book.)
i. How high is the cable 200 feet from the first tower? ii. What is the height of the cable above the water at its lowest point? 3. Fishing spiders can propel themselves across water and leap vertically from the surface of the water. During a vertical jump, the height of the body of the spider can be modeled by the function y = -4500x 2 + 820x + 43 where x is the duration (in seconds) of the jump and y is the height (in millimeters) of the spider above the surface of the water. i. Where is the maximum height shown in the graph? ii. What is the maximum height? ii. When does the spider reach its maximum height?
4. Students are selling packages of flower bulbs to raise money for a class trip. Last year, when the students charged $5 per package, they sold 150 packages. The students want to increase the cost per package. They estimate that they will lose 10 sales for each $1 increase in the cost per package. The sales revenue R (in dollars) generated by selling the packages is given by the function R = ( 5 + n )( 150 10n ) where n is the number of $1 increases. i. What will their revenue be if they make 3 ($1) increases? ii. Find the maximum revenue for this situation. iii. How many ($1) increases result in the maximum revenue? iv. What should the new price be? 5. The casts of some Broadway shows go on tour, performing their shows in cities across the United States. For the period 1990-2001, the number of tickets sold S (in millions) for Broadway road tours can be modeled by the function S = 332 + 132t 10.4t 2, where t is the number of years since 1990.
i. Use your equation to find the number of tickets sold in 1998. ii. In which year(s) did they sell 600 (million) tickets? iii. What year did they sell the most tickets? iv. How many tickets did they sell that year? 6. For the period 1971-2001, the number y of films produced in the world can be modeled by the function y = 10x 2 94x + 3900 where x is the number of years since 1971. i. Use your equation to find the number of films produced in the year 1981. ii. In what year(s) were 4200 films produced? iii. In what year(s) were 9000 films produced?
7. For the period 1990-2000, the amount of money y (in billions of dollars) spent on advertising in the U.S. can be modeled by the function y = 0.93x 2 + 2.2x + 130 where x is the number of years since 1990. i. How much money was spent on advertising in 1996? ii. In what year(s) was 164 billion dollars spent? 8. Between the months of April and September, the number y of hours of daylight per day in Seattle, Washington, can be modeled by the equation y = -0.00046x 2 + 0.076x + 13 where x is the number of days since April 1.
i. What is the x-value on April 19? Find the number of hours of daylight on April 19. ii. What is the x-value on July 4? Find the number of hours of daylight on July 4. iii. Which x-value(s) have 12 hours of daylight? What date(s) have 12 hours of daylight? iv. Do any of the days have 17 or more hours of daylight? If so, which ones? If not, explain. v. Do any of the days have 14 or more hours of daylight? If so, which ones? If not, explain.