Directions: Use your knowledge of properties of quadratic equations to answer each question. Show all work and label your answers with appropriate units. Round any decimals to the nearest hundredths place. 1. The hypotenuse of a right triangle is 5 centimeters longer than one leg and 10 centimeters longer than the other leg. What are the dimensions of the triangle? 2. The profit of a cell phone manufacturer is found by the function y = -2x²+ 108x+75, where x is the price of the cell phone. At what price should the manufacturer sell the phone to maximize its profits? What will the maximum profit be? 3. A farmer wants to build a fence around a rectangular area of his farm with one side of the region against his barn. He has 76 feet of fencing to use for the three remaining sides. What dimensions will make the largest area for the region? 4. A 13-foot ladder is leaning against a building, forming a right triangle. The height where the ladder touches the building is 7 feet more than the distance of the base of the ladder from the building. At what height does the ladder hit the building? 5. A basketball player throws the ball toward the basket and misses. The height of the ball is modeled by the function h(t)=-16t²+48t+6. What is the maximum height of the ball and when does the ball reach its maximum height? When will the ball hit the ground?
Directions: Use your knowledge of properties of quadratic equations to answer each question. Show all work and label your answers with appropriate units. Round any decimals to the nearest hundredths place. 1. The hypotenuse of a right triangle is 5 centimeters longer than one leg and 10 centimeters longer than the other leg. What are the dimensions of the triangle? 2. The profit of a cell phone manufacturer is found by the function y = -2x²+ 108x+75, where x is the price of the cell phone. At what price should the manufacturer sell the phone to maximize its profits? What will the maximum profit be? 3. A farmer wants to build a fence around a rectangular area of his farm with one side of the region against his barn. He has 76 feet of fencing to use for the three remaining sides. What dimensions will make the largest area for the region? 4. A 13-foot ladder is leaning against a building, forming a right triangle. The height where the ladder touches the building is 7 feet more than the distance of the base of the ladder from the building. At what height does the ladder hit the building? 5. A basketball player throws the ball toward the basket and misses. The height of the ball is modeled by the function h(t)=-16t²+48t+6. What is the maximum height of the ball and when does the ball reach its maximum height? When will the ball hit the ground?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.5: Solving Quadratic Equations By Completing The Square
Problem 27PPS
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Question
Transcribed Image Text:Directions: Use your knowledge of properties of quadratic equations to answer each question. Show all work and label your
answers with appropriate units. Round any decimals to the nearest hundredths place.
1. The hypotenuse of a right triangle is 5 centimeters longer than one leg and 10 centimeters longer than the other leg. What
are the dimensions of the triangle?
2. The profit of a cell phone manufacturer is found by the function y = -2x²+ 108x+75, where x is the price of the cell phone.
At what price should the manufacturer sell the phone to maximize its profits? What will the maximum profit be?
3. A farmer wants to build a fence around a rectangular area of his farm with one side of the region against his barn. He has 76
feet of fencing to use for the three remaining sides. What dimensions will make the largest area for the region?
4. A 13-foot ladder is leaning against a building, forming a right triangle. The height where the ladder touches the building is 7
feet more than the distance of the base of the ladder from the building. At what height does the ladder hit the building?
5. A basketball player throws the ball toward the basket and misses. The height of the ball is modeled by the function
h(t)=-16t²+48t+6. What is the maximum height of the ball and when does the ball reach its maximum height? When will the
ball hit the ground?
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