Factoring Quadratics: Real-Life Applications for 9th Grade

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 forming and factoring a quadratic equation.

• Width: 5 meters, Length: 8 meters

• Width: 8 meters, Length: 11 meters

• Width: 7 meters, Length: 10 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) = -5t^2 + 10t + 1.5. When will the ball hit the ground?

• t = 4.0 seconds

• t = 3.5 seconds

• t = 2.77 seconds

• t = 1.5 seconds

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

• 8 and 9

• 9 and 10

• 6 and 7

• 7 and 8

A company produces x units of a product, and the profit in dollars is given by the equation P(x) = -2x^2 + 40x - 100. How many units should the company produce to maximize profit?

• 15

• 5

• 10

• 20

A rectangular swimming pool has a length that is 4 meters longer than its width. If the perimeter of the pool is 48 meters, find the dimensions of the pool by forming and solving a quadratic equation.

• Width: 12 meters, Length: 16 meters

• Width: 8 meters, Length: 12 meters

• Width: 6 meters, Length: 10 meters

• Width: 10 meters, Length: 14 meters

The height of a projectile is modeled by the equation h(t) = -16t^2 + 32t + 5, where h is the height in feet and t is the time in seconds. How long will it take for the projectile to reach its maximum height?

• 1 second

• 2 seconds

• 3 seconds

• 0.5 seconds

A farmer wants to create a rectangular field with an area of 1200 square meters. If the length is 10 meters more than the width, find the dimensions of the field by forming and solving a quadratic equation.

• Width: 25 meters, Length: 35 meters

• Width: 20 meters, Length: 30 meters

• Width: 30 meters, Length: 40 meters

• Width: 15 meters, Length: 25 meters

The area of a triangle is given by the formula A = 1/2 * base * height. If the base is 2 meters longer than the height and the area is 30 square meters, find the base and height using a quadratic equation.

• Base: 7 meters, Height: 5 meters

• Base: 6 meters, Height: 4 meters

• Base: 8 meters, Height: 6 meters

• Base: 10 meters, Height: 5 meters

A rectangular box has a volume of 500 cubic centimeters. If the length is twice the width and the height is 5 centimeters, find the dimensions of the box by forming and solving a quadratic equation.

• Width: 10 cm, Length: 20 cm, Height: 5 cm

• Width: 5 cm, Length: 15 cm, Height: 5 cm

• Width: 4 cm, Length: 8 cm, Height: 5 cm

• Width: 5√2 cm, Length: 10√2 cm, Height: 5 cm

A car's value decreases according to the equation V(t) = -500t^2 + 20000, 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?

• 8 years

• 6.32 years

• 5 years

• 7.5 years