Quadratic Applications
Name: _____________________ Block: ____
This problem packet is due before 4pm on Friday, October 26. It is a formative assessment and worth 20
points. Complete the following problems. Circle or box your answer. Round decimals to the nearest
thousandth. Show ALL work on THIS paper. NO WORK = NO CREDIT!!!
Quadratic equations arise naturally when one solves problems from a variety of contexts, including area,
motion, economics, and growth rates of populations. In fact, any problem situation in which one quantity
depends upon the product of two linear quantities yields an analysis of a quadratic equation.
Read each question thoroughly to understand what is given and what is being asked.
1. The product of two consecutive positive even integers is 14 more than their sum. Find the integers.
2. Find three consecutive positive integers such that the product of the first two is 22 less than 11 times
the third.
3. The product of two consecutive odd integers is equal to 30 more than the first. Find the integers.
4. Find four consecutive integers such that the sum of the squares of the first two is 11 less than the
square of the fourth.
5. The length of a rectangle is 4 less than twice the width. The area of the rectangle is 70. Find the
dimensions of the rectangle.
6. A rectangular picture has a width that is two-thirds its length. The picture has an area of 294 square
inches. What are the dimensions of the picture?
7. A rectangle of length 2x 7 and width x has an area of 15 cm 2 . What is the length and width?
8. The perimeter of a square is (x) feet, and the area is (2x) square feet. Find the side length of the
square.
9. In a right triangle, the length of the longer leg is 7 more inches than the shorter leg. The length of the
hypotenuse is 8 more inches than the length of the shorter leg. Find all three side lengths.
10. Find the actual length of the hypotenuse of a right triangle given the lengths of the sides can be
modeled with (x) and (2x) and the length of the hypotenuse can be modeled with the expression (4 – x).
11. The longer leg of a right triangle is two inches more than twice the length of the shorter leg. The
hypotenuse is two inches less than three times the length of the shorter leg. Find the lengths of the three
sides of the triangle.
12. A miniature rocket is fired into the air and its path is modeled by the following formula where y is
the height in meters and x is the time in seconds: y 40x 4x 2 .
a. When is the rocket at a height of 64 meters?
b. How long is the rocket in the air?
13. An object is launched at 19.6 m/s from a 58.8 m tall platform. The equation for the object’s height,
h (meters), at time, t (seconds), after launch is h(t) 4.9t 2 19.6t 58.8 . When does the object strike
the ground?
1 2
t t 3, where h is height in meters, and t is
4
time is seconds. Algebraically determine how long it takes for the paper airplane to hit the ground.
14. A paper airplane follows a parabolic path with h
15. An object is launched straight up into the air at an initial velocity of 64 feet per second. It is launched
from a height of 6 feet off the ground. Its height H, in feet, at t seconds is given by the equation
H
16t 2 64t 6 . Find all times t that the object is at a height of 54 feet off the ground.
16. The height of a ball above the ground t seconds after it is thrown is h(t)
will it take for the ball to hit the ground?
16t 2
32t 5 . How long
17. An object is moving in a straight line. It initially travels at a speed of 9 meters per second, and it
speeds up at a constant rate of 2 meters per second each second. Under such conditions, the distance d, in
meters, that the object travels is given by the equation d = t 2 + 9t, where t is in seconds. According to this
equation, how long will it take the object to travel 22 meters?
18. The profit P, in dollars, gained by selling x computers is modeled by the equation
P
5x 2 1000x 5000. How many computers must be sold to obtain a profit of $55,000.00?
19. You have a rectangular piece of sheet metal that needs to be made into an open box (no lid). The
length is twice the width. The depth of the box must be 2 inches and the box must hold approximately
100 cubic inches of sand when filled evenly to the top. To do this, you will be taking a rectangular piece
of sheet metal, cutting squares from each corner, and folding up the edges. What are the dimensions of
the sheet metal you will need to accomplish this task ?
20. An open box (no lid) made from a rectangular piece of sheet metal must be 6 inches deep and have a
volume of 3000 cubic inches. The length of the sheet metal is one and a half times as long as its width.
Find the dimensions of the original piece of sheet metal.