Real-Life Quadratic Challenges: Graphing & 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, what are the dimensions of the garden?

• Width: 5 meters, Length: 8 meters

• Width: 3 meters, Length: 6 meters

• Width: 6 meters, Length: 9 meters

• Width: 4 meters, Length: 7 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 can be modeled by the equation h(t) = -5t^2 + 10t + 1.5. When will the ball hit the ground?

• 2 seconds

• 3 seconds

• 5 seconds

• 4 seconds

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

• 7 and 8

• 6 and 7

• 8 and 9

• 9 and 10

A rectangular pool is being built with a length that is twice its width. If the area of the pool is 200 square feet, what are the dimensions of the pool?

• Length: 20 feet, Width: 10 feet

• Length: 25 feet, Width: 12.5 feet

• Length: 30 feet, Width: 15 feet

• Length: 15 feet, Width: 7.5 feet

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

• 3

• 1

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 triangle.

• Height: 10 meters, Base: 14 meters

• Height: 8 meters, Base: 12 meters

• Height: 6 meters, Base: 10 meters

• Height: 9 meters, Base: 13 meters

A projectile is launched from the ground with an initial velocity of 20 meters per second. The height of the projectile can be modeled by the equation h(t) = -4.9t^2 + 20t. When will the projectile reach its maximum height?

• 4.1 seconds

• 1.5 seconds

• 3.0 seconds

• 2.04 seconds

A rectangular piece of land has a length that is 5 meters longer than its width. If the area of the land is 60 square meters, what are the dimensions of the land?

• Width: 7 meters, Length: 12 meters

• Width: 4 meters, Length: 8 meters

• Width: 6 meters, Length: 9 meters

• Width: 5 meters, Length: 10 meters

The difference of the squares of two consecutive integers is 1. What are the integers?

• 2 and 3

• 0 and 1

• -1 and 0

• 1 and 2

A farmer has a rectangular field where the length is 10 meters more than twice the width. If the area of the field is 300 square meters, what are the dimensions of the field?

• Width: 15 meters, Length: 40 meters

• Width: 10 meters, Length: 30 meters

• Width: 5 meters, Length: 20 meters

• Width: 12 meters, Length: 34 meters