Quadratics in Real Life: Solving & Factoring Challenges

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? (Use the quadratic formula)

• Width: 7 meters, Length: 10 meters

• Width: 8 meters, Length: 11 meters

• Width: 6 meters, Length: 9 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. The height of the ball in meters after t seconds is given by the equation h(t) = -4.9t^2 + 10t + 1.5. When will the ball hit the ground? (Use the quadratic formula)

• 1.75 seconds

• 4.50 seconds

• 3.00 seconds

• 2.36 seconds

The path of a projectile is modeled by the equation h(t) = -16t^2 + 32t + 48, where h is the height in feet and t is the time in seconds. At what time will the projectile reach its maximum height? (Factor the quadratic expression)

• 1 second

• 3 seconds

• 0.5 seconds

• 2 seconds

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? (Use the quadratic formula)

• 25

• 20

• 15

• 10

The area of a triangular field is 120 square meters. If the base is 4 meters longer than the height, find the dimensions of the field. (Set up a quadratic equation and factor)

• Height: 10 meters, Base: 14 meters

• Height: 8 meters, Base: 12 meters

• Height: 15 meters, Base: 19 meters

• Height: 12 meters, Base: 16 meters

A car's value V (in dollars) after t years is given by the equation V(t) = -2000t^2 + 12000t + 15000. How many years will it take for the car's value to drop to $10,000? (Use the quadratic formula)

• 3.78

• 2.50

• 4.00

• 5.10

The height of a water fountain is modeled by the equation h(t) = -3t^2 + 12t + 5, where h is the height in meters and t is the time in seconds. When will the fountain reach its maximum height? (Factor the quadratic expression)

• 2 seconds

• 4 seconds

• 1 second

• 3 seconds

A rectangular swimming pool has a length that is 2 meters longer than its width. If the perimeter of the pool is 40 meters, what are the dimensions of the pool? (Set up and solve a quadratic equation)

• Width: 10 meters, Length: 12 meters

• Width: 8 meters, Length: 10 meters

• Width: 7 meters, Length: 9 meters

• Width: 9 meters, Length: 11 meters

A farmer wants to create a rectangular pen for his sheep. He has 100 meters of fencing. If the length of the pen is 10 meters longer than the width, what are the dimensions of the pen? (Use the quadratic formula)

• Width: 15 meters, Length: 25 meters

• Width: 25 meters, Length: 35 meters

• Width: 30 meters, Length: 40 meters

• Width: 20 meters, Length: 30 meters

The height of a projectile is modeled by the equation h(t) = -16t^2 + 64t + 80. How long will it take for the projectile to hit the ground? (Use the quadratic formula)

• 7 seconds

• 3 seconds

• 10 seconds

• 5 seconds