Finding Roots: Real-Life Quadratic Challenges

A gardener is planting a rectangular flower bed. The area of the bed is 144 square feet, and the length is 12 feet. What is the width of the flower bed?

• 10 feet

• 14 feet

• 16 feet

• 12 feet

A ball is thrown into the air, and its height in feet can be modeled by the equation h(t) = -16t^2 + 32t + 48, where t is the time in seconds. What are the times when the ball hits the ground?

• 4 seconds

• 2 seconds

• 3 seconds

• 5 seconds

A rectangular pool has a length that is 3 feet longer than its width. If the area of the pool is 54 square feet, what are the dimensions of the pool?

• Width: 6 feet, Length: 9 feet

• Width: 7 feet, Length: 10 feet

• Width: 4 feet, Length: 7 feet

• Width: 5 feet, Length: 8 feet

The path of a projectile can be modeled by the equation h(t) = -4.9t^2 + 20t + 5. Find the time when the projectile reaches its maximum height.

• 1.50 seconds

• 2.04 seconds

• 3.00 seconds

• 4.10 seconds

A square garden has an area of 64 square meters. What is the length of one side of the garden?

• 6 meters

• 12 meters

• 8 meters

• 10 meters

A car's distance from a starting point can be modeled by the equation d(t) = t^2 - 6t + 8. At what times does the car return to the starting point?

• t = 0, t = 5

• t = 2, t = 4

• t = 1, t = 3

• t = 2, t = 6

A rectangular field has a perimeter of 60 meters. If the length is 5 meters more than the width, what are the dimensions of the field?

• Width: 12.5 meters, Length: 17.5 meters

• Width: 10 meters, Length: 15 meters

• Width: 20 meters, Length: 25 meters

• Width: 5 meters, Length: 10 meters

The height of a ball thrown upwards can be modeled by the equation h(t) = -5t^2 + 20t + 15. Determine the time when the ball reaches the ground.

• t = 4 - √7

• t = 2 + √7 or t = 2 - √7 (only t = 2 + √7 is valid)

• t = 1 + √7

• t = 3

A rectangular box has a volume of 120 cubic inches. If the length is twice the width and the height is 3 inches, what is the width of the box?

• 5

• 4

• 3

• 2√5

A farmer has a triangular plot of land with a base of 10 meters and a height of 6 meters. If the area of the plot is given by the formula A = 1/2 * base * height, what is the area of the plot?

• 25 square meters

• 15 square meters

• 20 square meters

• 30 square meters