Solving Quadratic Word Problems: Factors & Interpretations

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?

• Width: 8 meters, Length: 11 meters

• Width: 6 meters, Length: 9 meters

• Width: 5 meters, Length: 8 meters

• Width: 7 meters, Length: 10 meters

A ball is thrown upwards from a height of 1.5 meters with an initial velocity of 12 meters per second. The height of the ball in meters after t seconds is given by the equation h(t) = -4.9t^2 + 12t + 1.5. When will the ball hit the ground?

• 3.0 seconds

• 4.5 seconds

• 2.5 seconds

• 1.0 seconds

The product of two consecutive integers is 72. What are the integers?

• 8 and 9

• 9 and 10

• 7 and 8

• 6 and 7

A rectangular pool is 4 meters longer than it is wide. If the area of the pool is 96 square meters, what are the dimensions of the pool?

• Width: 6 meters, Length: 10 meters

• Width: 8 meters, Length: 12 meters

• Width: 5 meters, Length: 9 meters

• Width: 10 meters, Length: 14 meters

A company produces a certain product at a cost represented by the equation C(x) = 2x^2 - 8x + 24, where x is the number of units produced. How many units should the company produce to minimize costs?

• 1

• 2

• 3

• 5

The height of a projectile is modeled by the equation h(t) = -16t^2 + 32t + 48. At what time will the projectile reach its maximum height?

• 0

• 2

• 3

• 1

A farmer wants to create a rectangular field with a perimeter of 100 meters. If the length is 5 meters more than the width, what are the dimensions of the field?

• Width: 15 meters, Length: 20 meters

• Width: 22.5 meters, Length: 27.5 meters

• Width: 20 meters, Length: 30 meters

• Width: 25 meters, Length: 30 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, what are the base and height of the triangle?

• Base: 8 meters, Height: 6 meters

• Base: 7 meters, Height: 5 meters

• Base: 6 meters, Height: 4 meters

• Base: 10 meters, Height: 5 meters

A rectangular box has a volume of 120 cubic centimeters. If the length is twice the width and the height is 3 centimeters less than the width, what are the dimensions of the box?

• Width: 6 cm, Length: 12 cm, Height: 3 cm

• Width: 8 cm, Length: 16 cm, Height: 6 cm

• Width: 5 cm, Length: 10 cm, Height: 4 cm

• Width: 7 cm, Length: 14 cm, Height: 5 cm

A car's value decreases according to the equation V(t) = -500t^2 + 5000, 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?

• Approximately 3.16 years

• 2.5 years

• 4.0 years

• 5.5 years