Mastering Quadratic Equations: Identify and Solve Challenges

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. What is the maximum height the ball reaches?

• 10 meters

• 7 meters

• 3 meters

• 5 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: 5 meters, Length: 8 meters

• Width: 6 meters, Length: 9 meters

• Width: 3 meters, Length: 6 meters

• Width: 4 meters, Length: 7 meters

A car's distance from a starting point is modeled by the equation d(t) = -4t^2 + 20t, where d is in meters and t is in seconds. How long will it take for the car to return to the starting point?

• 5 seconds

• 7 seconds

• 3 seconds

• 10 seconds

The path of a projectile is modeled by the equation h(t) = -16t^2 + 32t + 5. At what time will the projectile hit the ground?

• 2.5

• 4.0

• 1.5

• 3.0

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?

• 20

• 5

• 10

• 15

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: 15 meters, Length: 30 meters

• Width: 10 meters, Length: 20 meters

• Width: 8 meters, Length: 16 meters

The height of a water fountain is modeled by the equation h(t) = -3t^2 + 12t + 1. What is the height of the fountain after 2 seconds?

• 13

• 8

• 15

• 10

A farmer wants to create a rectangular field with a perimeter of 100 meters. If the length is represented as x meters, express the area A of the field as a quadratic equation and find the maximum area.

• 750 square meters

• 625 square meters

• 400 square meters

• 500 square meters

A rock is thrown into the air, and its height in meters after t seconds is given by h(t) = -4.9t^2 + 20t + 1. How long will it take for the rock to reach its maximum height?

• 2.75 seconds

• 2.04 seconds

• 1.50 seconds

• 3.00 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, find the dimensions of the box.

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

• Width: 6 cm, Length: 8 cm, Height: 3 cm

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

• Width: 5 cm, Length: 7 cm, Height: 3 cm