Maximize Heights and Areas: Quadratic Functions Quiz

A ball is thrown upwards from a height of 2 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 + 2. What is the maximum height reached by the ball?

• 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: 3 meters, Length: 6 meters

• Width: 6 meters, Length: 9 meters

• Width: 5 meters, Length: 8 meters

• Width: 4 meters, Length: 7 meters

A company finds that the profit P (in dollars) from selling x items is given by the equation P(x) = -2x^2 + 12x - 10. How many items should the company sell to maximize its profit?

• 3

• 4

• 5

• 2

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

• 3.2 seconds

• 4.08 seconds

• 2.5 seconds

• 6.0 seconds

A farmer wants to create a rectangular pen with an area of 120 square meters. If the length of the pen is 5 meters more than its width, what are the dimensions of the pen?

• Width: 8 meters, Length: 20 meters

• Width: 12 meters, Length: 17 meters

• Width: 5 meters, Length: 25 meters

• Width: 10 meters, Length: 15 meters

The height of a water fountain is modeled by the equation h(t) = -3t^2 + 15t, where h is the height in meters and t is the time in seconds. What is the height of the fountain at 2 seconds?

• 12 meters

• 24 meters

• 18 meters

• 6 meters

A toy rocket is launched, and its height in meters after t seconds is given by the equation h(t) = -4.9t^2 + 30t. What is the time when the rocket reaches its maximum height?

• 5.0 seconds

• 4.2 seconds

• 2.5 seconds

• 3.06 seconds

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

• Length: 30 meters, Width: 15 meters

• Length: 25 meters, Width: 12.5 meters

• Length: 15 meters, Width: 7.5 meters

• Length: 20 meters, Width: 10 meters

The revenue R (in dollars) from selling x units of a product is given by the equation R(x) = -3x^2 + 30x. What is the maximum revenue the company can achieve?

• 60

• 100

• 75

• 90

A car's distance from a starting point is modeled by the equation d(t) = -2t^2 + 16t, where d is the distance in meters and t is the time in seconds. At what time does the car return to the starting point?

• 4 seconds

• 8 seconds

• 12 seconds

• 10 seconds