Solving Quadratic Word Problems in Real-Life Scenarios

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: 5 meters, Length: 8 meters

• Width: 8 meters, Length: 11 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 high will the ball go before it starts to fall back down?

• 6.6 meters

• 5.0 meters

• 4.5 meters

• 8.2 meters

The path of a projectile can be modeled by the equation h(t) = -4.9t^2 + 20t + 1.5, where h is the height in meters and t is the time in seconds. What is the maximum height reached by the projectile?

• 21.58 meters

• 19.5 meters

• 15.3 meters

• 25.0 meters

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

• 10

• 20

• 5

• 15

A car's distance from a starting point can be modeled by the equation d(t) = 5t^2 + 10t, where d is the distance in meters and t is the time in seconds. How far will the car be after 3 seconds?

• 45 meters

• 90 meters

• 75 meters

• 60 meters

The height of a water fountain can be modeled by the equation h(t) = -16t^2 + 32t + 5, where h is the height in feet and t is the time in seconds. At what time will the fountain reach its maximum height?

• 0 seconds

• 2 seconds

• 1 second

• 3 seconds

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: 8 meters, Length: 16 meters

• Width: 5 meters, Length: 10 meters

• Width: 15 meters, Length: 30 meters

• Width: 10 meters, Length: 20 meters

A rock is thrown from a cliff and its height above the ground can be modeled by the equation h(t) = -16t^2 + 64t + 80. How long will it take for the rock to hit the ground?

• 4 seconds

• 3 seconds

• 2 seconds

• 1 second

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

• Base: 10 meters, Height: 14 meters

• Base: 8 meters, Height: 12 meters

• Base: 6 meters, Height: 10 meters

• Base: 5 meters, Height: 9 meters

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, what are the dimensions of the box?

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

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

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

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