Real-Life Quadratic Word Problems: Solve & Analyze

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: 7 meters, Length: 10 meters

• Width: 6 meters, Length: 9 meters

• Width: 8 meters, Length: 11 meters

• Width: 5 meters, Length: 8 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?

• 3.00 seconds

• 1.75 seconds

• 4.50 seconds

• 2.14 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?

• 0.75 seconds

• 1.50 seconds

• 1.02 seconds

• 2.00 seconds

A company produces a certain product and finds that the profit, P, in thousands of dollars, can be modeled by the equation P(x) = -2x^2 + 12x - 10, where x is the number of units sold in thousands. How many units should they sell to maximize profit?

• 4

• 5

• 1

• 3

A car's speed is modeled by the equation s(t) = -5t^2 + 20t + 15, where s is the speed in meters per second and t is the time in seconds. When will the car come to a stop?

• t = 0.5 seconds

• t = 1.5 seconds

• t = 2 seconds

• t = 3 seconds

The height of a water fountain can be modeled by the equation h(t) = -16t^2 + 32t + 5. How long will the water reach a height of 10 feet?

• 0.5 seconds and 2.0 seconds

• 0.15 seconds and 2.85 seconds

• 1.0 seconds and 2.0 seconds

• 1.5 seconds and 3.5 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: 10 meters, Length: 20 meters

• Width: 5 meters, Length: 10 meters

• Width: 15 meters, Length: 30 meters

• Width: 8 meters, Length: 16 meters

A farmer wants to create a rectangular field with a fixed 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 dimensions that maximize the area.

• Length = 40 meters, Width = 10 meters

• Length = 50 meters, Width = 0 meters

• Length = 25 meters, Width = 25 meters

• Length = 30 meters, Width = 20 meters

A toy rocket is launched from a height of 2 meters with an initial velocity of 15 meters per second. How long will it take for the rocket to reach the ground?

• 4.10 seconds

• 3.25 seconds

• 2.01 seconds

• 1.50 seconds

The area of a triangular plot of land is given by the equation A = 0.5 * base * height. If the base is represented as x and the height is x + 4, find the value of x when the area is 48 square meters.

• 12

• 8

• 10

• 6