Real-Life Quadratics: Maximizing Area and Profit

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. 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?

• 2.24 seconds

• 4.50 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. When will the projectile reach its maximum height?

• 3 seconds

• 1 second

• 0.5 seconds

• 2 seconds

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

• 15

• 25

• 20

• 10

The area of a triangular park is represented by the equation A = 0.5 * base * height. If the base is represented as a quadratic expression b(x) = x^2 + 4x and the height is constant at 5 meters, what is the area of the park as a function of x?

• A(x) = 2.5x + 10

• A(x) = 2.5x^2 + 10x

• A(x) = 0.5x^2 + 2.5x

• A(x) = 5x^2 + 20x

A car's distance from a starting point can be modeled by the equation d(t) = -4.9t^2 + 20t, where d is in meters and t is in seconds. How far will the car travel before it stops?

• 20.41 meters

• 25.0 meters

• 15.5 meters

• 10.2 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: 8 feet, Length: 16 feet

• Width: 12 feet, Length: 24 feet

• Width: 10 feet, Length: 20 feet

• Width: 15 feet, Length: 30 feet

The height of a projectile is modeled by the equation h(t) = -16t^2 + 64t + 80. What is the time when the projectile reaches the ground?

• 5

• 7

• 6

• 4

A farmer wants to create a rectangular field with a fixed perimeter of 100 meters. What dimensions will maximize the area of the field?

• 20 meters by 30 meters

• 25 meters by 25 meters

• 10 meters by 40 meters

• 15 meters by 35 meters

The revenue R from selling x units of a product is given by R(x) = -2x^2 + 40x. How many units should be sold to maximize revenue?

• 5

• 15

• 10

• 20