Quadratic Equations in Real Life: Application & Factoring

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: 5 meters, Length: 8 meters

• Width: 8 meters, Length: 11 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 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. When will the projectile reach its maximum height?

• 1 second

• 1.5 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) = -2x^2 + 40x - 100. How many items should the company sell to maximize its profit?

• 10

• 20

• 5

• 15

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 park using a quadratic equation.

• Height: 14 meters, Base: 16 meters

• Height: 10 meters, Base: 12 meters

• Height: 20 meters, Base: 22 meters

• Height: 8 meters, Base: 10 meters

A car's distance from a starting point is modeled by the equation d(t) = 5t^2 + 20t, where d is in meters and t is in seconds. How far will the car be from the starting point after 4 seconds?

• 200 meters

• 160 meters

• 80 meters

• 120 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? Factor the quadratic expression to find the width.

• Width: 10 feet, Length: 20 feet

• Width: 15 feet, Length: 30 feet

• Width: 12 feet, Length: 24 feet

• Width: 8 feet, Length: 16 feet

The height of a projectile is modeled by the equation h(t) = -16t^2 + 64t + 80. Determine the time when the projectile will reach the ground by applying the quadratic formula.

• 10 seconds

• 7 seconds

• 3 seconds

• 5 seconds

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 factoring to solve the quadratic equation.

• Width: 20 meters, Length: 30 meters

• Width: 10 meters, Length: 20 meters

• Width: 25 meters, Length: 35 meters

• Width: 15 meters, Length: 25 meters

The area of a rectangular plot is represented by the equation A = x(x + 5) = 60, where x is the width. Find the width of the plot by factoring the quadratic expression.

• 5

• 20

• 15

• 10