Quadratic Equations: Solving Real-World Problems

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 70 square meters, what are the dimensions of the garden?

• Width: 8 meters, Length: 11 meters

• Width: 6 meters, Length: 9 meters

• Width: 7 meters, Length: 10 meters

• Width: 5 meters, Length: 8 meters

A ball is thrown upwards from a height of 1.5 meters with an initial velocity of 10 meters per second. The height of the ball in meters after t seconds is given by the equation h(t) = -4.9t^2 + 10t + 1.5. How long will it take for the ball to hit the ground?

• 1.75 seconds

• 3.10 seconds

• 2.24 seconds

• 4.50 seconds

The path of a projectile can be modeled by the equation h(t) = -16t^2 + 32t + 48, where h is the height in feet and t is the time in seconds. At what time will the projectile reach its maximum height?

• 3

• 1

• 0.5

• 2

A company finds that the profit P (in dollars) from selling x items is given by the equation P(x) = -5x^2 + 150x - 200. How many items should the company sell to maximize its profit?

• 15

• 25

• 10

• 20

A car's speed is modeled by the equation s(t) = -2t^2 + 20t, where s is the speed in meters per second and t is the time in seconds. What is the maximum speed of the car?

• 60 m/s

• 50 m/s

• 30 m/s

• 40 m/s

The height of a water fountain can be modeled by the equation h(t) = -3t^2 + 12t, where h is the height in meters and t is the time in seconds. How long will it take for the water to reach a height of 0 meters?

• 6 seconds

• 4 seconds

• 2 seconds

• 8 seconds

A rectangular swimming pool has a length that is 4 meters longer than its width. If the area of the pool is 96 square meters, what are the dimensions of the pool?

• Width: 8 meters, Length: 12 meters

• Width: 5 meters, Length: 9 meters

• Width: 6 meters, Length: 10 meters

• Width: 10 meters, Length: 14 meters

A farmer wants to create a rectangular field with a perimeter of 100 meters. If the length is 5 meters more than the width, what are the dimensions of the field?

• Width: 15 meters, Length: 20 meters

• Width: 22.5 meters, Length: 27.5 meters

• Width: 25 meters, Length: 30 meters

• Width: 20 meters, Length: 30 meters

The height of a ball thrown into the air is modeled by the equation h(t) = -16t^2 + 64t + 5. How long will the ball be in the air before it hits the ground?

• 3.2 seconds

• 5.0 seconds

• 2.5 seconds

• 4.06 seconds

A rectangular box has a volume of 120 cubic centimeters. If the length is twice the width and the height is 3 centimeters, what are the dimensions of the box?

• Width: 3 cm, Length: 6 cm, Height: 4 cm

• Width: 1 cm, Length: 2 cm, Height: 60 cm

• Width: 2√5 cm, Length: 4√5 cm, Height: 3 cm

• Width: 5 cm, Length: 10 cm, Height: 2 cm