Real-Life Quadratic Challenges: Graphing & Factoring

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is 40 square meters, what are the dimensions of the garden?

• Width: 4 meters, Length: 7 meters

• Width: 5 meters, Length: 8 meters

• Width: 3 meters, Length: 6 meters

• Width: 6 meters, Length: 9 meters

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 can be modeled by the equation h(t) = -5t^2 + 10t + 2. When will the ball hit the ground?

• 1.25 seconds

• 0.75 seconds

• 0.30 seconds

• 0.54 seconds

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

• 8 and 9

• 7 and 8

• 6 and 7

• 9 and 10

A company produces a certain product and finds that the profit, P, in dollars, can be modeled by the equation P(x) = -2x^2 + 8x - 10, where x is the number of units sold. How many units must be sold to maximize profit?

• 2

• 5

• 1

• 3

A rectangular pool has a length that is twice its width. If the area of the pool is 200 square meters, what are the dimensions of the pool?

• Width: 5 meters, Length: 10 meters

• Width: 8 meters, Length: 16 meters

• Width: 10 meters, Length: 20 meters

• Width: 15 meters, Length: 30 meters

The height of a projectile is modeled by the equation h(t) = -4.9t^2 + 20t + 5. How long will it take for the projectile to reach its maximum height?

• 4.2 seconds

• 1.5 seconds

• 3.0 seconds

• 2.04 seconds

A farmer has a rectangular field with an area of 1500 square meters. If the length is 10 meters more than the width, what are the dimensions of the field?

• Width: 35 meters, Length: 45 meters

• Width: 25 meters, Length: 35 meters

• Width: 20 meters, Length: 30 meters

• Width: 30 meters, Length: 40 meters

The area of a triangular plot of land is given by the equation A = 1/2 * base * height. If the base is 4 meters longer than the height and the area is 48 square meters, what are the dimensions of the triangle?

• Height: 10 meters, Base: 14 meters

• Height: 5 meters, Base: 9 meters

• Height: 8 meters, Base: 12 meters

• Height: 6 meters, Base: 10 meters

A car's value decreases according to the equation V(t) = -500t^2 + 3000, where V is the value in dollars and t is the time in years. When will the car's value reach zero?

• 1.5 years

• Approximately 2.45 years

• 3.0 years

• 4.2 years

A rectangular box has a volume of 120 cubic centimeters. If the length is 2 centimeters longer than the width and the height is 3 centimeters, what are the dimensions of the box?

• Width: 10 cm, Length: 12 cm, Height: 3 cm

• Width: 6 cm, Length: 8 cm, Height: 3 cm

• Width: 5 cm, Length: 7 cm, Height: 3 cm

• Width: 4 cm, Length: 6 cm, Height: 3 cm