Real-World Quadratics: Solve & Interpret Contexts

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: 6 meters, Length: 9 meters

• Width: 8 meters, Length: 11 meters

• Width: 5 meters, Length: 8 meters

• Width: 7 meters, Length: 10 meters

A ball is thrown upwards from a height of 1.5 meters with an initial velocity of 10 meters per second. How long will it take for the ball to hit the ground?

• 1.75 seconds

• 3.00 seconds

• 2.12 seconds

• 4.50 seconds

The path of a projectile can be modeled by the equation h(t) = -4.9t^2 + 10t + 1.5, where h is the height in meters and t is the time in seconds. When will the projectile reach its maximum height?

• 1.02 seconds

• 0.75 seconds

• 2.00 seconds

• 1.50 seconds

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

• 5

• 20

• 15

• 10

A swimming pool is being filled with water. The volume of water in the pool can be modeled by the equation V(t) = -t^2 + 20t, where V is the volume in cubic meters and t is the time in hours. When will the pool be full if its capacity is 100 cubic meters?

• The pool will be full in 15 hours.

• The pool will never be full.

• The pool will be full in 5 hours.

• The pool will be full in 10 hours.

A farmer wants to create a rectangular pen for his sheep. He has 60 meters of fencing. If the length of the pen is 5 meters more than its width, what are the dimensions of the pen?

• Width: 20 meters, Length: 25 meters

• Width: 12.5 meters, Length: 17.5 meters

• Width: 15 meters, Length: 20 meters

• Width: 10 meters, Length: 15 meters

A rock is thrown from a cliff and its height above the ground can be modeled by the equation h(t) = -5t^2 + 20t + 30. How long will it take for the rock to reach the ground?

• 5.16

• 4.25

• 7.10

• 6.00

The area of a triangular park is given by the equation A = 0.5 * base * height. If the base is 4 meters longer than the height and the area is 48 square meters, what are the dimensions of the park?

• Height: 8 meters, Base: 12 meters

• Height: 5 meters, Base: 9 meters

• Height: 10 meters, Base: 14 meters

• Height: 6 meters, Base: 10 meters

A rectangular box has a volume of 120 cubic centimeters. The length is twice the width, and the height is 3 centimeters less than the width. What are the dimensions of the box?

• Width: 4 cm, Length: 8 cm, Height: 1 cm

• Width: 8 cm, Length: 16 cm, Height: 5 cm

• Width: 5 cm, Length: 10 cm, Height: 2 cm

• Width: 6 cm, Length: 12 cm, Height: 3 cm

A car's distance from a starting point can be modeled by the equation d(t) = -2t^2 + 12t, where d is the distance in meters and t is the time in seconds. When will the car return to the starting point?

• 4 seconds

• 8 seconds

• 6 seconds

• 10 seconds