Real-Life Quadratics: Interpreting Word Problems

A ball is thrown upwards from a height of 2 meters with an initial velocity of 10 meters per second. The height of the ball after t seconds is given by the equation h(t) = -5t^2 + 10t + 2. How long will it take for the ball to hit the ground?

• 3.74 seconds

• 4.20 seconds

• 2.50 seconds

• 5.00 seconds

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: 5 meters, Length: 8 meters

• Width: 7 meters, Length: 10 meters

A company finds that the profit P (in dollars) from selling x units of a product can be modeled by the equation P(x) = -2x^2 + 40x - 100. How many units should the company sell to maximize its profit?

• 20

• 5

• 10

• 15

The path of a projectile is modeled by the equation h(t) = -4.9t^2 + 20t + 5, where h is the height in meters and t is the time in seconds. At what time will the projectile reach its maximum height?

• 1.50 seconds

• 2.04 seconds

• 3.00 seconds

• 4.10 seconds

A car's distance from a starting point can be modeled by the equation d(t) = 3t^2 + 12t, where d is the distance in meters and t is the time in seconds. How far will the car be from the starting point after 4 seconds?

• 84 meters

• 120 meters

• 96 meters

• 72 meters

A farmer wants to create a rectangular pen for his sheep using 100 meters of fencing. If the length of the pen is x meters, what is the maximum area that can be enclosed, and what are the dimensions of the pen?

• Maximum area: 625 square meters; Dimensions: 25 meters by 25 meters.

• Maximum area: 700 square meters; Dimensions: 30 meters by 30 meters.

• Maximum area: 500 square meters; Dimensions: 20 meters by 25 meters.

• Maximum area: 400 square meters; Dimensions: 10 meters by 40 meters.

The height of a water fountain can be modeled by the equation h(t) = -16t^2 + 32t, where h is the height in feet and t is the time in seconds. How long will it take for the water to reach a height of 24 feet?

• The water will reach 24 feet in 2 seconds.

• The water will never reach a height of 24 feet.

• The water will reach 24 feet in 1 second.

• The water will reach a height of 24 feet at t = 0.5 seconds.

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: 8 meters, Length: 16 meters

• Width: 15 meters, Length: 30 meters

A toy rocket is launched from a height of 10 meters with an initial velocity of 15 meters per second. The height of the rocket after t seconds is given by the equation h(t) = -4.9t^2 + 15t + 10. When will the rocket reach its maximum height?

• 2.00 seconds

• 0.75 seconds

• 1.53 seconds

• 1.25 seconds

A rectangular field has a perimeter of 60 meters. If the length is 5 meters longer than the width, what are the dimensions of the field?

• Width: 15 meters, Length: 20 meters

• Width: 5 meters, Length: 10 meters

• Width: 10 meters, Length: 15 meters

• Width: 12.5 meters, Length: 17.5 meters