Real-Life Quadratics: Solving and Factoring Fun!

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 to find the width.

• Width: 7 meters, Length: 10 meters

• Width: 8 meters, Length: 11 meters

• Width: 5 meters, Length: 8 meters

• Width: 6 meters, Length: 9 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?

• 1.75 seconds

• 2.24 seconds

• 3.10 seconds

• 4.50 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?

• 0.5 seconds

• 1 second

• 2 seconds

• 3 seconds

A company produces a certain product, and the profit in dollars can be modeled by the equation P(x) = -2x^2 + 12x - 16, where x is the number of units sold. How many units should the company sell to maximize profit?

• 4

• 5

• 2

• 3

The area of a triangular park is 120 square meters. If the base of the triangle is 2 meters longer than its height, find the dimensions of the triangle using a quadratic equation.

• Height: 8 meters, Base: 10 meters

• Height: 14 meters, Base: 16 meters

• Height: 10 meters, Base: 12 meters

• Height: 20 meters, Base: 22 meters

A car's value decreases over time and can be modeled by the equation V(t) = -500t^2 + 3000, where V is the value in dollars and t is the time in years. After how many years will the car's value be zero?

• 4.2 years

• 3.0 years

• 1.5 years

• Approximately 2.45 years

A rectangular swimming pool has a length that is twice its width. If the area of the pool is 200 square meters, find the dimensions of the pool by factoring the quadratic expression.

• Width: 15 meters, Length: 30 meters

• Width: 8 meters, Length: 16 meters

• Width: 5 meters, Length: 10 meters

• Width: 10 meters, Length: 20 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 solve.

• Width: 22.5 meters, Length: 27.5 meters

• Width: 20 meters, Length: 30 meters

• Width: 15 meters, Length: 20 meters

• Width: 25 meters, Length: 30 meters

The height of a projectile is modeled by the equation h(t) = -5t^2 + 20t + 15. Determine the time at which the projectile will reach the ground.

• 6.000

• 4.645

• 5.200

• 3.500

A rectangular box has a volume of 120 cubic centimeters. If the length is 4 centimeters longer than the width and the height is 3 centimeters, find the dimensions of the box using a quadratic equation.

• Width: 6 cm, Length: 10 cm, Height: 3 cm

• Width: 7 cm, Length: 11 cm, Height: 3 cm

• Width: 5 cm, Length: 9 cm, Height: 4 cm

• Width: 8 cm, Length: 12 cm, Height: 2 cm