Application Problems Quadratic Equations
UNIT 6 (2) NOTES Quadratic Applications
Application Problems
Quadratic Equations
There are several standard types of problems: * Problems with given formula * Falling object problems * Geometric shapes
UNIT 6 (2) NOTES Quadratic Applications
The number of bacteria in refrigerated food is given by and where T is the temperature for of the food in Celsius. At what temperature will the number of bacteria be minimal?
A model rocket is launched from the roof of a building. Its flight path is modeled by the equation below where h is the height of the rocket above the ground in meters and t is the time in seconds after the launch. What is the maximum height of the rocket?
UNIT 6 (2) NOTES Quadratic Applications
The height,h,in feet of an object above the when ground is where t is the time in seconds. Find the time it takes the object to strike the ground.
A model rocket is projected straight upward from the ground level according to the height equation where h is the height in feet and t is the time in seconds. At what time is the rocket at its maximum? What is the maximum height of the rocket?
UNIT 6 (2) NOTES Quadratic Applications
In the Pro Bowl, NFL punter Ray Guy of the Oakland Raiders kicked a ball so high it hit the scoreboard hanging from the roof of the New Orleans Superdome (forcing the officials to raise the scoreboard from 90 ft to 200 ft. If we assume the ball made contact with the scoreboard near the apex of the kick, the function is one possible model for the height of the ball where h(t) represents the height in feet after t seconds. A) What does the y-intercept represent? B) After how many seconds did the football reach the maximum height? C) What was the maximum height? D) To the nearest second what was the hang time of the ball? (How long the ball was in the air.)
The length of a Ping-Pong table is 3 ft more than twice the width. The area the table is 90 square feet. What are the dimensions of the Ping-Pong table?
UNIT 6 (2) NOTES Quadratic Applications
Two equal rectangular corrals are to be made from 100 yards of fencing as seen below. If the rancher wants the total area to be maximized, what dimensions should be used to make the corrals?
Three hundred feet of fencing is available to enclose a rectangular yard along the St. John's River, which is used as one side of the rectangle. What is the maximum area that can be enclosed?
UNIT 6 (2) NOTES Quadratic Applications
Tickets to an off broadway play cost $40.00 each. The projected attendance per night is 3000 people. For every $1.00 increase in the ticket, the manager believes 50 less people will attend. What is the greatest possible revenue for a single night's performance? What ticket price will produce the greatest revenue?
Application Problems
Quadratic Equations
There are several standard types of problems: * Problems with given formula * Falling object problems * Geometric shapes
UNIT 6 (2) NOTES Quadratic Applications
The number of bacteria in refrigerated food is given by and where T is the temperature for of the food in Celsius. At what temperature will the number of bacteria be minimal?
A model rocket is launched from the roof of a building. Its flight path is modeled by the equation below where h is the height of the rocket above the ground in meters and t is the time in seconds after the launch. What is the maximum height of the rocket?
UNIT 6 (2) NOTES Quadratic Applications
The height,h,in feet of an object above the when ground is where t is the time in seconds. Find the time it takes the object to strike the ground.
A model rocket is projected straight upward from the ground level according to the height equation where h is the height in feet and t is the time in seconds. At what time is the rocket at its maximum? What is the maximum height of the rocket?
UNIT 6 (2) NOTES Quadratic Applications
In the Pro Bowl, NFL punter Ray Guy of the Oakland Raiders kicked a ball so high it hit the scoreboard hanging from the roof of the New Orleans Superdome (forcing the officials to raise the scoreboard from 90 ft to 200 ft. If we assume the ball made contact with the scoreboard near the apex of the kick, the function is one possible model for the height of the ball where h(t) represents the height in feet after t seconds. A) What does the y-intercept represent? B) After how many seconds did the football reach the maximum height? C) What was the maximum height? D) To the nearest second what was the hang time of the ball? (How long the ball was in the air.)
The length of a Ping-Pong table is 3 ft more than twice the width. The area the table is 90 square feet. What are the dimensions of the Ping-Pong table?
UNIT 6 (2) NOTES Quadratic Applications
Two equal rectangular corrals are to be made from 100 yards of fencing as seen below. If the rancher wants the total area to be maximized, what dimensions should be used to make the corrals?
Three hundred feet of fencing is available to enclose a rectangular yard along the St. John's River, which is used as one side of the rectangle. What is the maximum area that can be enclosed?
UNIT 6 (2) NOTES Quadratic Applications
Tickets to an off broadway play cost $40.00 each. The projected attendance per night is 3000 people. For every $1.00 increase in the ticket, the manager believes 50 less people will attend. What is the greatest possible revenue for a single night's performance? What ticket price will produce the greatest revenue?
