Quadratic Word Problems

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Show your work for each problem.

1.
A ball is thrown upward. Its height in meters after seconds is . When does the ball hit the ground?
1. a)After 5 seconds
2. b)After 10 seconds
3. c)After 4 seconds
4. d)After 2 seconds
2.
The product of two consecutive positive integers is 72. What are the integers?
1. a)8 and 9
2. b)9 and 10
3. c)6 and 12
4. d)7 and 8
3.
A rectangular garden has length 3 meters more than its width. If the area is 40 square meters, what is the width (in meters)?
4.
The sum of a number and its square is 56. What is the positive number?
5.
Which type of quadratic word problem is this? 'A rocket's height is . Find the maximum height.'
1. a)Optimization problem
2. b)Consecutive integer problem
3. c)Area problem
4. d)Number problem
6.
A ball is thrown upward with initial velocity 30 m/s from ground level. Its height is . Find the maximum height.
7.
A rectangle has perimeter 30 cm. What width (in cm) maximizes the area?
8.
The height of a ball is . At what time does it reach maximum height?
1. a)1 second
2. b)2 seconds
3. c)4 seconds
4. d)3 seconds
9.
Find two consecutive even integers whose product is 168.
10.
A picture frame is 2 cm wide on all sides. The picture inside is 8 cm by 6 cm. What is the total area of the frame (including picture) in square cm?
11.
A company's profit (in euros) is where is units sold. What is the break-even point (where )?
1. a)10 and 60 units
2. b)25 and 75 units
3. c)20 and 80 units
4. d)30 and 70 units
12.
A ball is thrown from a 20-meter building with initial velocity 15 m/s upward. Its height is . When does it hit the ground?
13.
A rocket's height is . What is its maximum height in meters?
14.
A theater charges 25 euros per ticket and sells 400 tickets. For each 5 euro increase, they sell 20 fewer tickets. What price maximizes revenue?
15.
A ball thrown from height 10 m follows . When does it reach 40 meters?
1. a)Never reaches 40 m
2. b)At 1 second only
3. c)At 2 and 3 seconds
4. d)At 1.5 and 4 seconds
16.
Two numbers differ by 5. Their product is 126. Find the larger number.