Factoring Quadratics: Real-Life Applications for 9th Graders

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 70 square meters, find the dimensions of the garden by factoring the quadratic equation.

• Width: 7 meters, Length: 10 meters

• Width: 6 meters, Length: 9 meters

• Width: 8 meters, Length: 11 meters

• Width: 5 meters, Length: 8 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) = -5t^2 + 10t + 1.5. Find the time when the ball hits the ground by factoring.

• 2 seconds

• 4 seconds

• 3 seconds

• 5 seconds

The product of two consecutive integers is 72. Find the integers by setting up and factoring a quadratic equation.

• 7 and 8

• 6 and 7

• 9 and 10

• 8 and 9

A company produces x units of a product, and the profit in dollars is given by the equation P(x) = -2x^2 + 40x - 96. Determine the number of units that need to be produced to maximize profit by factoring the quadratic equation.

• 8

• 6

• 12

• 10

The area of a triangle is given by the formula A = 1/2 * base * height. If the base is 4 meters longer than the height and the area is 48 square meters, find the dimensions of the triangle by factoring the resulting quadratic equation.

• Height: 5 meters, Base: 9 meters

• Height: 8 meters, Base: 12 meters

• Height: 10 meters, Base: 14 meters

• Height: 6 meters, Base: 10 meters

A rectangular pool has a length that is twice its width. If the area of the pool is 288 square meters, find the dimensions of the pool by factoring the quadratic equation.

• Width: 10 meters, Length: 20 meters

• Width: 15 meters, Length: 30 meters

• Width: 12 meters, Length: 24 meters

• Width: 8 meters, Length: 16 meters

A projectile is launched from the ground with an initial velocity of 20 meters per second. The height of the projectile after t seconds is given by h(t) = -5t^2 + 20t. Find the time when the projectile reaches its maximum height by factoring the quadratic equation.

• 4 seconds

• 2 seconds

• 3 seconds

• 1 second

The difference between the squares of two consecutive integers is 1. Find the integers by setting up and factoring a quadratic equation.

• 0 and 1

• 1 and 2

• 2 and 3

• -1 and 0

A farmer wants to create a rectangular field with a perimeter of 100 meters. If the length is 10 meters more than the width, find the dimensions of the field by factoring the quadratic equation.

• Width: 10 meters, Length: 20 meters

• Width: 25 meters, Length: 35 meters

• Width: 15 meters, Length: 25 meters

• Width: 20 meters, Length: 30 meters

A rectangular piece of land has a length that is 5 meters longer than its width. If the area of the land is 60 square meters, find the dimensions of the land by factoring the quadratic equation.

• Width: 5 meters, Length: 10 meters

• Width: 4 meters, Length: 9 meters

• Width: 6 meters, Length: 11 meters

• Width: 7 meters, Length: 12 meters