Quadratic Equations and Formula: Real-World Applications

A ball is thrown upwards from a height of 5 meters with an initial velocity of 10 m/s. The height of the ball after t seconds is given by the equation h(t) = -5t^2 + 10t + 5. What is the maximum height the ball reaches?

• 5 meters

• 10 meters

• 15 meters

• 20 meters

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 40 square meters, what are the dimensions of the garden?

• Width: 4 meters, Length: 7 meters

• Width: 5 meters, Length: 8 meters

• Width: 3 meters, Length: 6 meters

• Width: 6 meters, Length: 9 meters

The path of a projectile is modeled by the equation h(t) = -4.9t^2 + 20t + 1, where h is the height in meters and t is the time in seconds. When will the projectile hit the ground?

• 4.08 seconds

• 3.5 seconds

• 5.2 seconds

• 6.0 seconds

A company finds that the profit P (in dollars) from selling x items is given by the equation P(x) = -2x^2 + 40x - 50. How many items should the company sell to maximize its profit?

• 15

• 5

• 10

• 20

A car's distance from a starting point is modeled by the equation d(t) = 2t^2 + 3t + 1. How far is the car from the starting point after 2 seconds?

• 10

• 5

• 15

• 20

The height of a water fountain can be modeled by the equation h(t) = -16t^2 + 32t + 5. At what time will the fountain reach its maximum height?

• 0

• 2

• 1

• 3

A rectangular swimming pool has a length that is twice its width. If the area of the pool is 200 square meters, what are the dimensions of the pool?

• Width: 5 meters, Length: 10 meters

• Width: 10 meters, Length: 20 meters

• Width: 15 meters, Length: 30 meters

• Width: 8 meters, Length: 16 meters

A rock is thrown into the air, and its height in meters after t seconds is given by the equation h(t) = -4.9t^2 + 20t + 10. How long will it take for the rock to hit the ground?

• 4.56 seconds

• 6.75 seconds

• 5.10 seconds

• 3.25 seconds

The area of a triangular plot of land is given by the equation A = 1/2 * base * height. If the base is 4 meters longer than the height and the area is 48 square meters, what are the dimensions of the triangle?

• Height: 5 meters, Base: 9 meters

• Height: 8 meters, Base: 12 meters

• Height: 10 meters, Base: 14 meters

• Height: 6 meters, Base: 10 meters

A rectangular box has a volume of 120 cubic centimeters. If the length is 5 cm longer than the width and the height is 2 cm, what are the dimensions of the box?

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

• Width: 6 cm, Length: 11 cm, Height: 2 cm

• Width: 4 cm, Length: 9 cm, Height: 3 cm

• Width: 5 cm, Length: 8 cm, Height: 4 cm