Real Roots & Word Problems: Quadratic Applications Quiz

A ball is thrown upwards from a height of 5 meters with an initial velocity of 20 meters per second. How long will it take for the ball to hit the ground?

• 4.24 seconds

• 5.50 seconds

• 6.75 seconds

• 3.10 seconds

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: 5 meters, Length: 8 meters

• Width: 6 meters, Length: 9 meters

• Width: 4 meters, Length: 7 meters

A company finds that the profit from selling x items can be modeled by the equation P(x) = -2x^2 + 40x - 50. How many items should they sell to maximize their profit?

• 5

• 20

• 10

• 15

The path of a projectile can be 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. When will the projectile hit the ground?

• 6.75 seconds

• 5.10 seconds

• 3.25 seconds

• 4.56 seconds

A car's distance from a starting point can be modeled by the equation d(t) = -5t^2 + 30t, where d is the distance in meters and t is the time in seconds. How long will it take for the car to return to the starting point?

• 10 seconds

• 4 seconds

• 8 seconds

• 6 seconds

A rectangular swimming pool has a length that is 2 meters longer than its width. If the area of the pool is 50 square meters, what are the dimensions of the pool?

• Width: 5.45 meters, Length: 7.45 meters

• Width: 5 meters, Length: 7 meters

• Width: 4 meters, Length: 6 meters

• Width: 6 meters, Length: 8 meters

The height of a basketball thrown into the air can be modeled by the equation h(t) = -16t^2 + 32t + 6. At what time will the basketball reach its maximum height?

• 2

• 1

• 0

• 3

A farmer wants to create a rectangular field with a perimeter of 100 meters. If the length is 10 meters longer than the width, what are the dimensions of the field?

• Width: 25 meters, Length: 35 meters

• Width: 20 meters, Length: 30 meters

• Width: 15 meters, Length: 25 meters

• Width: 30 meters, Length: 40 meters

A rock is thrown from a height of 10 meters with an initial velocity of 15 meters per second. How long will it take for the rock to reach the ground?

• 3.10 seconds

• 2.34 seconds

• 0.75 seconds

• 1.57 seconds

The area of a triangular plot of land is given by the equation A = 1/2 * base * height. If the base is represented by the equation b = x^2 - 4x + 4, what is the height when the area is 12 square meters?

• 18

• 6

• 24

• 30