Quadratic Word Challenges: Contextual Solutions & Formulas

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 40 square meters, find the dimensions of the garden using the factored form of the quadratic equation.

• Width: 3 meters, Length: 6 meters

• Width: 6 meters, Length: 9 meters

• Width: 4 meters, Length: 7 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. Determine when the ball will hit the ground.

• t = 1.5 seconds

• t = 4.2 seconds

• t = 2.78 seconds

• t = 3.5 seconds

The product of two consecutive integers is 72. Find the integers by setting up a quadratic equation in factored form.

• 9 and 10

• 6 and 7

• 8 and 9

• 7 and 8

A company produces a certain product and finds that their profit, P, in thousands of dollars, can be modeled by the equation P(x) = -2(x - 5)(x + 3), where x is the number of units sold in thousands. How many units must be sold to break even?

• 10000

• 3000

• 5000

• 7000

A rectangular swimming pool has a length that is 4 meters longer than its width. If the area of the pool is 96 square meters, find the dimensions of the pool using the quadratic formula.

• Width: 5 meters, Length: 9 meters

• Width: 6 meters, Length: 10 meters

• Width: 10 meters, Length: 14 meters

• Width: 8 meters, Length: 12 meters

The height of a projectile is modeled by the equation h(t) = -16t^2 + 32t + 48. Determine the time when the projectile reaches its maximum height and interpret the result in the context of the problem.

• 0.5 seconds

• 2 seconds

• 1 second

• 3 seconds

A farmer wants to create a rectangular pen for his sheep. He has 100 meters of fencing. If the length of the pen is 10 meters longer than its width, find the dimensions of the pen using a quadratic equation in factored form.

• Width: 25 meters, Length: 35 meters

• Width: 30 meters, Length: 40 meters

• Width: 20 meters, Length: 30 meters

• Width: 15 meters, Length: 25 meters

The area of a triangular plot of land is 60 square meters. If the base is 4 meters longer than the height, find the dimensions of the plot using the quadratic formula.

• Height: 8 meters, Base: 12 meters

• Height: 6 meters, Base: 10 meters

• Height: 10 meters, Base: 14 meters

• Height: 5 meters, Base: 9 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, find the dimensions of the box using a quadratic equation.

• Width: 7 cm, Length: 14 cm, Height: 4 cm

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

• Width: 4 cm, Length: 8 cm, Height: 1 cm

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

A car's distance from a starting point is modeled by the equation d(t) = -4t^2 + 20t + 5, where d is in meters and t is in seconds. Determine when the car will return to the starting point and interpret the solution contextually.

• The car returns to the starting point at 2.5 seconds and 5.5 seconds.

• The car returns to the starting point at 1.5 seconds and 6.5 seconds.

• The car never returns to the starting point.

• The car returns to the starting point at approximately 0.64 seconds and 7.86 seconds.