Solving Word Problems with Quadratic Functions

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: 8 meters, Length: 11 meters

• Width: 6 meters, Length: 9 meters

• Width: 5 meters, Length: 8 meters

• Width: 7 meters, Length: 10 meters

A ball is thrown upwards from a height of 5 meters with an initial velocity of 20 meters per second. The height of the ball after t seconds is given by the equation h(t) = -5t^2 + 20t + 5. When will the ball hit the ground?

• Approximately 5.0 seconds

• Approximately 2.0 seconds

• Approximately 4.24 seconds

• Approximately 3.5 seconds

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

• 7 and 8

• 9 and 10

• 8 and 9

• 6 and 7

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

• 10

• 20

• 15

A rectangular pool is to be built with a length that is twice its width. If the area of the pool is 288 square feet, what are the dimensions of the pool?

• Width: 12 feet, Length: 24 feet

• Width: 8 feet, Length: 16 feet

• Width: 15 feet, Length: 30 feet

• Width: 10 feet, Length: 20 feet

The height of a projectile is modeled by the equation h(t) = -16t^2 + 64t + 80. How long will it take for the projectile to reach its maximum height?

• 3 seconds

• 2 seconds

• 4 seconds

• 1 second

A farmer has a field in the shape of a rectangle. The length is 4 meters less than twice the width. If the area of the field is 96 square meters, what are the dimensions of the field?

• Width: 10 meters, Length: 16 meters

• Width: 8 meters, Length: 12 meters

• Width: 4 meters, Length: 8 meters

• Width: 6 meters, Length: 10 meters

A quadratic function is represented by the equation y = x^2 - 6x + 8. What are the x-intercepts of the function?

• x = -2, x = -4

• x = 2, x = 4

• x = 1, x = 5

• x = 0, x = 6

The area of a triangular plot of land is given by the equation A = 1/2 * base * height. If the base is represented by the expression (x + 4) and the height is represented by (x - 2), find the area when x = 6.

• 18

• 30

• 20

• 12

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

• 1.5 years

• 3.0 years

• Approximately 2.45 years

• 4.2 years