Solving Word Problems in Quadratics: Grade 9 Challenge

A ball is thrown upwards from a height of 2 meters with an initial velocity of 10 meters per second. The height of the ball after t seconds is given by the equation h(t) = -5t^2 + 10t + 2. How long will it take for the ball to hit the ground?

• 3.74 seconds

• 5.00 seconds

• 4.20 seconds

• 2.50 seconds

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: 6 meters, Length: 9 meters

• Width: 7 meters, Length: 10 meters

• Width: 5 meters, Length: 8 meters

• Width: 8 meters, Length: 11 meters

A company finds that the profit P (in dollars) from selling x items is given by the equation P(x) = -2x^2 + 40x - 100. How many items should the company sell to maximize its profit?

• 5

• 15

• 10

• 20

The path of a projectile is modeled by the equation h(t) = -4.9t^2 + 20t + 5, where h is the height in meters and t is the time in seconds. At what time will the projectile reach its maximum height?

• 1.50 seconds

• 3.00 seconds

• 2.04 seconds

• 4.10 seconds

A car's distance from a starting point is modeled by the equation d(t) = 3t^2 + 12t, where d is in meters and t is in seconds. How far will the car be from the starting point after 4 seconds?

• 96 meters

• 120 meters

• 72 meters

• 84 meters

A rectangular swimming pool has a width that is 2 meters less than its length. If the area of the pool is 48 square meters, what are the dimensions of the pool?

• Length: 5 meters, Width: 3 meters

• Length: 10 meters, Width: 8 meters

• Length: 6 meters, Width: 4 meters

• Length: 8 meters, Width: 6 meters

The height of a water fountain is modeled by the equation h(t) = -16t^2 + 32t + 1. How long will it take for the water to reach a height of 0 meters?

• 2.5 seconds

• 3 seconds

• 1.5 seconds

• 4 seconds

A farmer wants to create a rectangular pen for his sheep. The length of the pen is 4 meters more than twice the width. If the area of the pen is 96 square meters, what are the dimensions of the pen?

• Width: 6 meters, Length: 16 meters

• Width: 5 meters, Length: 14 meters

• Width: 8 meters, Length: 20 meters

• Width: 4 meters, Length: 12 meters

A toy rocket is launched from a height of 1 meter with an initial velocity of 15 meters per second. The height of the rocket after t seconds is given by h(t) = -4.9t^2 + 15t + 1. When will the rocket reach its maximum height?

• 1.25 seconds

• 0.75 seconds

• 2.00 seconds

• 1.53 seconds

A rectangular plot of land has a length that is 5 meters longer than its width. If the perimeter of the plot is 50 meters, what are the dimensions of the plot?

• Width: 12 meters, Length: 17 meters

• Width: 10 meters, Length: 15 meters

• Width: 5 meters, Length: 10 meters

• Width: 8 meters, Length: 13 meters