Factoring Quadratic Equations: Real-World Applications

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden can be expressed as a quadratic equation in factored form, what are the dimensions of the garden if the area is 40 square meters?

• Width: 4 meters, Length: 7 meters

• Width: 6 meters, Length: 9 meters

• Width: 3 meters, Length: 6 meters

• Width: 5 meters, Length: 8 meters

The product of two consecutive integers is 72. Write a quadratic equation in factored form to represent this situation and find the integers.

• 9 and 10

• The integers are 8 and 9.

• 6 and 7

• 7 and 8

A ball is thrown upwards from a height of 5 meters with an initial velocity of 20 meters per second. The height of the ball can be modeled by a quadratic equation. What is the height of the ball when it reaches its maximum height?

• 20.5 meters

• 30.0 meters

• 25.4 meters

• 15.2 meters

A company produces a certain product and finds that their profit can be modeled by the equation P(x) = -2(x - 5)(x + 3), where x is the number of units sold. How many units must they sell to break even?

• 5

• 10

• 7

• 3

The area of a triangular plot of land is represented by the equation A(x) = (x - 2)(x + 4). What are the possible values of x that represent the base of the triangle?

• x = -2

• x = 0

• x <= -4 or x >= 2

• x > -4 and x < 2

A rectangular swimming pool has a length that is twice its width. If the area of the pool is 200 square meters, write a quadratic equation in factored form to find the dimensions of the pool.

• (w - 5)(w + 5) = 0

• (w - 10)(w + 10) = 0

• (w - 20)(w + 10) = 0

• (w - 15)(w + 15) = 0

A farmer has a rectangular field where the length is 4 meters more than twice the width. If the area of the field is 96 square meters, what are the dimensions of the field?

• Width: 4 meters, Length: 12 meters

• Width: 6 meters, Length: 16 meters

• Width: 8 meters, Length: 20 meters

• Width: 5 meters, Length: 14 meters

The height of a projectile can be modeled by the equation h(t) = -16(t - 2)(t - 5), where t is the time in seconds. At what times does the projectile hit the ground?

• t = 2 seconds and t = 5 seconds

• t = 1 second

• t = 3 seconds

• t = 6 seconds

A rectangular box has a volume of 120 cubic centimeters. If the length is 2 centimeters more than the width and the height is 3 centimeters, write a quadratic equation in factored form to find the width of the box.

• (w + 5)(w - 6) = 0

• (w + 8)(w - 2) = 0

• (w + 12)(w - 10) = 0

• (w + 10)(w - 4) = 0

A concert hall has a seating arrangement where the number of seats can be represented by the equation S(x) = (x - 10)(x + 5). What are the possible values of x that represent the number of rows of seats?

• 5

• 15

• 20

• 10