Real-Life Quadratics: Solving with the Quadratic Formula

A ball is thrown upwards from a height of 2 meters with an initial velocity of 10 m/s. How long will it take for the ball to hit the ground? Use the quadratic formula to find the time.

• 1.5 seconds

• 2.08 seconds

• 4.2 seconds

• 3.0 seconds

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 40 square meters, what are the dimensions of the garden? Use the quadratic formula to solve for the width.

• Width: 5 meters, Length: 8 meters

• Width: 3 meters, Length: 6 meters

• Width: 4 meters, Length: 7 meters

• Width: 6 meters, Length: 9 meters

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

• 25

• 20

• 10

• 15

The path of a projectile is modeled by the equation h(t) = -4.9t^2 + 20t + 5, where h is the height in meters and t is the time in seconds. When will the projectile hit the ground? Use the quadratic formula to find the time.

• 3.25 seconds

• 5.10 seconds

• 4.56 seconds

• 6.00 seconds

A car's distance from a starting point is modeled by the equation d(t) = 2t^2 + 3t, where d is in meters and t is in seconds. How long will it take for the car to travel 30 meters? Use the quadratic formula to solve for t.

• 3.77 seconds

• 2.50 seconds

• 5.00 seconds

• 4.20 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? Use the quadratic formula to find the width and length.

• Width: 10 meters, Length: 20 meters

• Width: 15 meters, Length: 30 meters

• Width: 5 meters, Length: 10 meters

• Width: 8 meters, Length: 16 meters

The height of a triangle is 4 meters less than its base. If the area of the triangle is 48 square meters, what are the dimensions of the base and height? Use the quadratic formula to solve for the base.

• Base: 10 meters, Height: 6 meters

• Base: 14 meters, Height: 10 meters

• Base: 16 meters, Height: 12 meters

• Base: 12 meters, Height: 8 meters

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? Use the quadratic formula to find the width and length.

• Width: 25 meters, Length: 35 meters

• Width: 10 meters, Length: 20 meters

• Width: 20 meters, Length: 30 meters

• Width: 15 meters, Length: 25 meters

A toy rocket is launched from a height of 1 meter with an initial velocity of 15 m/s. The height of the rocket after t seconds is given by h(t) = -4.9t^2 + 15t + 1. When will the rocket reach its maximum height? Use the quadratic formula to find the time.

• 2.10 seconds

• 1.25 seconds

• 1.53 seconds

• 0.75 seconds

A rectangular plot of land has a length that is 5 meters longer than its width. If the area of the plot is 60 square meters, what are the dimensions of the plot? Use the quadratic formula to find the width and length.

• Width: 6 meters, Length: 11 meters

• Width: 7 meters, Length: 12 meters

• Width: 5 meters, Length: 10 meters

• Width: 4 meters, Length: 9 meters