Factoring Quadratics: Real-Life Applications for Grade 9

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?

• Width: 6 meters, Length: 9 meters

• Width: 5 meters, Length: 8 meters

• Width: 5 meters, Length: 10 meters

• Width: 4 meters, Length: 7 meters

A ball is thrown into the air, and its height in meters after t seconds is given by the equation h(t) = -5t^2 + 20t. What is the maximum height the ball reaches?

• 25 meters

• 15 meters

• 20 meters

• 10 meters

The area of a rectangular field is represented by the quadratic equation A = x^2 + 5x - 24. Factor the equation to find the possible dimensions of the field.

• (x + 10) and (x - 2)

• (x + 6) and (x - 4)

• (x + 5) and (x - 5)

• The possible dimensions of the field are (x + 8) and (x - 3).

A company produces x units of a product, and the profit in dollars is given by the equation P(x) = -2x^2 + 8x + 10. What is the maximum profit the company can achieve?

• 18

• 10

• 15

• 20

A triangular piece of land has a base that is 2 meters longer than its height. If the area of the triangle is 30 square meters, find the height and base of the triangle.

• Height: 6 meters, Base: 8 meters

• Height: 10 meters, Base: 12 meters

• Height: 4 meters, Base: 6 meters

• Height: 5 meters, Base: 7 meters

The path of a projectile is modeled by the equation h(t) = -4.9t^2 + 20t, where h is the height in meters and t is the time in seconds. How long does it take for the projectile to hit the ground?

• 2.5 seconds

• 6.0 seconds

• 3.2 seconds

• 4.08 seconds

A rectangular pool has a length that is twice its width. If the area of the pool is 72 square meters, what are the dimensions of the pool?

• Width: 4 meters, Length: 8 meters

• Width: 3 meters, Length: 6 meters

• Width: 6 meters, Length: 12 meters

• Width: 5 meters, Length: 10 meters

A farmer has a rectangular plot of land with an area of 50 square meters. If the length is 5 meters longer than the width, find the dimensions of the plot.

• Width: 4 meters, Length: 9 meters

• Width: 5 meters, Length: 10 meters

• Width: 5 meters, Length: 8 meters

• Width: 6 meters, Length: 11 meters

The area of a square is represented by the equation A = x^2. If the area is 64 square meters, what is the length of one side of the square?

• 8 meters

• 12 meters

• 10 meters

• 6 meters

A car's value decreases according to the equation V(t) = -3t^2 + 12t + 20, where V is the value in thousands of dollars and t is the time in years. When will the car's value be zero?

• 7.10 years

• 5.55 years

• 4.00 years

• 3.25 years