Maximizing Heights & Areas: Quadratic Equations Quiz

A ball is thrown upwards from a height of 5 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 + 5. What is the maximum height the ball reaches?

• 5 meters

• 10 meters

• 20 meters

• 15 meters

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 54 square meters, what are the dimensions of the garden?

• Width: 5 meters, Length: 8 meters

• Width: 4 meters, Length: 7 meters

• Width: 7 meters, Length: 10 meters

• Width: 6 meters, Length: 9 meters

A company finds that the profit P (in dollars) from selling x items is given by the equation P(x) = -2x^2 + 40x - 100. How many items should the company sell to maximize its profit?

• 20

• 15

• 5

• 10

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. At what time does the projectile hit the ground?

• 4.08 seconds

• 6.0 seconds

• 3.5 seconds

• 5.2 seconds

A car's distance from a starting point is modeled by the equation d(t) = 2t^2 + 3t, where d is in meters and t is in seconds. How far is the car from the starting point after 5 seconds?

• 65 meters

• 80 meters

• 100 meters

• 50 meters

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: 10 meters, Length: 14 meters

• Width: 6 meters, Length: 10 meters

• Width: 8 meters, Length: 12 meters

• Width: 5 meters, Length: 9 meters

The height of a water fountain is modeled by the equation h(t) = -3t^2 + 12t + 5. What is the time at which the fountain reaches its maximum height?

• 1

• 4

• 2

• 3

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

• 500 square meters

• 750 square meters

• 400 square meters

• 625 square 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 h(t) = -4.9t^2 + 15t + 10. When will the rocket reach its maximum height?

• 0.75 seconds

• 2.00 seconds

• 1.53 seconds

• 1.25 seconds

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

• Width: 8 meters, Length: 16 meters

• Width: 5 meters, Length: 10 meters

• Width: 15 meters, Length: 30 meters

• Width: 10 meters, Length: 20 meters