Factoring Quadratics: Real-Life Applications for 9th Grade

A rectangular garden has an area of 48 square meters. If the length of the garden is 2 meters more than its width, find the dimensions of the garden by factoring the quadratic equation.

• Width: 4 meters, Length: 12 meters

• Width: 6 meters, Length: 8 meters

• Width: 7 meters, Length: 9 meters

• Width: 5 meters, Length: 10 meters

A ball is thrown into the air, and its height in meters can be modeled by the equation h(t) = -4t^2 + 16t, where t is the time in seconds. Factor the equation to find the time when the ball hits the ground.

• 8 seconds

• 6 seconds

• 2 seconds

• 4 seconds

The area of a triangular park is represented by the equation A = x^2 + 5x - 14. Factor the trinomial to find the possible values of x that represent the base of the triangle.

• -2, 7

• -5, 3

• -7, 2

• 1, 14

A company produces a certain product, and the profit in dollars can be modeled by the equation P(x) = x^2 - 9x + 20. Factor the equation to find the number of units sold that will result in zero profit.

• 2 and 7

• 1 and 8

• 4 and 5

• 3 and 6

A rectangular swimming pool has a length that is 3 meters longer than its width. If the area of the pool is 70 square meters, write a quadratic equation, factor it, and find the dimensions of the pool.

• Width: 4 meters, Length: 7 meters

• Width: 6 meters, Length: 9 meters

• Width: 7 meters, Length: 10 meters

• Width: 5 meters, Length: 8 meters

The height of a projectile is modeled by the equation h(t) = -t^2 + 6t - 8. Factor the equation to determine the times when the projectile reaches a height of zero.

• t = 2

• t = 8

• t = 6

• t = 4

A farmer wants to fence a rectangular field with an area of 120 square meters. If the length is 4 meters longer than the width, write a quadratic equation, factor it, and find the dimensions of the field.

• Width: 8 meters, Length: 12 meters

• Width: 5 meters, Length: 9 meters

• Width: 6 meters, Length: 10 meters

• Width: 10 meters, Length: 14 meters

The area of a rectangular poster is represented by the equation A = x^2 + 7x + 10. Factor the trinomial to find the possible dimensions of the poster.

• (x + 1)(x + 10)

• (x + 2)(x + 5)

• (x + 3)(x + 4)

• (x + 2)(x + 6)

A rectangular plot of land has a length that is twice its width. If the area of the plot is 200 square meters, write a quadratic equation, factor it, and find the dimensions of the plot.

• Width: 15 meters, Length: 30 meters

• Width: 10 meters, Length: 20 meters

• Width: 5 meters, Length: 10 meters

• Width: 8 meters, Length: 16 meters

A basketball is thrown from a height of 5 feet, and its height can be modeled by the equation h(t) = -16t^2 + 10t + 5. Factor the equation to find the time when the basketball hits the ground.

• 0

• 2

• 3

• 1