Solving Real-Life Quadratics: Equations & Applications

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: 8 meters, Length: 11 meters

• Width: 6 meters, Length: 9 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. The height of the ball in meters after t seconds is given by the equation h(t) = -4.9t^2 + 10t + 1.5. How long will it take for the ball to hit the ground?

• 4.50 seconds

• 2.24 seconds

• 3.10 seconds

• 1.75 seconds

The path of a projectile can be modeled by the equation h(t) = -16t^2 + 32t + 48, where h is the height in feet and t is the time in seconds. What is the maximum height reached by the projectile?

• 80 feet

• 48 feet

• 56 feet

• 64 feet

A company finds that the profit P (in dollars) from selling x items is given by the equation P(x) = -5x^2 + 150x - 200. How many items should the company sell to maximize its profit?

• 25

• 20

• 15

• 10

The area of a triangular park is represented by the equation A = 0.5 * base * height. If the base is 2 meters less than twice the height, and the area is 50 square meters, find the dimensions of the park.

• Height: 12 meters, Base: 22 meters

• Height: 8 meters, Base: 14 meters

• Height: 5 meters, Base: 10 meters

• Height: 10 meters, Base: 18 meters

A car's distance from a starting point can be modeled by the equation d(t) = 5t^2 + 20t, where d is the distance in meters and t is the time in seconds. How far will the car be after 4 seconds?

• 80 meters

• 120 meters

• 160 meters

• 200 meters

A rectangular swimming pool has a length that is twice its width. If the area of the pool is 288 square feet, what are the dimensions of the pool?

• Width: 15 feet, Length: 30 feet

• Width: 10 feet, Length: 20 feet

• Width: 12 feet, Length: 24 feet

• Width: 8 feet, Length: 16 feet

The height of a water fountain can be modeled by the equation h(t) = -4.9t^2 + 20t, where h is the height in meters and t is the time in seconds. How long will the water reach the ground?

• 3.5 seconds

• 4.08 seconds

• 6.0 seconds

• 5.2 seconds

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

• Length: 25 meters, Width: 15 meters

• Length: 40 meters, Width: 30 meters

• Length: 20 meters, Width: 10 meters

• Length: 30 meters, Width: 20 meters

The height of a basketball when thrown can be modeled by the equation h(t) = -16t^2 + 32t + 5. How long will it take for the basketball to reach its maximum height?

• 0.5 seconds

• 2 seconds

• 3 seconds

• 1 second