Mastering Quadratics: Solving Real-World Problems

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.

• 1.50 seconds

• 3.00 seconds

• 2.08 seconds

• 4.25 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? Solve using the quadratic formula.

• Width: 4 meters, Length: 7 meters

• Width: 6 meters, Length: 9 meters

• Width: 3 meters, Length: 6 meters

• Width: 5 meters, Length: 8 meters

A company finds that the profit from selling x items is given by the equation P(x) = -2x^2 + 40x - 100. How many items should the company sell to maximize profit? Use the quadratic formula to find the number of items.

• 5

• 10

• 20

• 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? Apply the quadratic formula to determine the time.

• t ≈ 2.34 seconds

• t ≈ 4.56 seconds

• t ≈ 6.78 seconds

• t ≈ 3.12 seconds

A car's distance from a starting point is modeled by the equation d(t) = 5t^2 + 10t, where d is in meters and t is in seconds. How long will it take for the car to reach 100 meters? Use the quadratic formula to solve.

• 8.3 seconds

• 4.1 seconds

• 6.0 seconds

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

• Width: 8 meters, Length: 16 meters

• Width: 15 meters, Length: 30 meters

• Width: 10 meters, Length: 20 meters

• Width: 5 meters, Length: 10 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 triangle? Solve using the quadratic formula.

• Base: 10 meters, Height: 6 meters

• Base: 14 meters, Height: 10 meters

• Base: 12 meters, Height: 8 meters

• Base: 16 meters, Height: 12 meters

A farmer wants to create a rectangular field with a perimeter of 100 meters. If the length is 5 meters more than the width, what are the dimensions of the field? Use the quadratic formula to find the width and length.

• Width: 22.5 meters, Length: 27.5 meters

• Width: 15 meters, Length: 20 meters

• Width: 20 meters, Length: 30 meters

• Width: 25 meters, Length: 30 meters

A projectile is launched from the ground with an initial velocity of 30 m/s. The height of the projectile is modeled by the equation h(t) = -4.9t^2 + 30t. When will the projectile reach its maximum height? Use the quadratic formula to find the time.

• 4.00 seconds

• 3.06 seconds

• 2.50 seconds

• 5.20 seconds

The area of a square is represented by the equation A = x^2 + 6x + 8. What is the side length of the square? Use the quadratic formula to find the value of x.

• 8

• 6

• 2

• 4