Real-Life Polynomial Problems: Solve & Graph Functions

A rectangular garden has a length that is 3 meters longer than its width. If the area of the garden is represented by the polynomial A = x(x + 3), where x is the width, find the width of the garden by solving the polynomial equation.

• x can be any positive value, typically we would need a specific area to find a unique width.

• The width is 3 meters.

• The area is 6 square meters.

• The width must be 0 meters.

The height of a triangular prism is represented by the polynomial h = 2x^2 + 3x - 5, where x is the base length. Graph the polynomial function to find the height when the base length is 2 meters.

• 11 meters

• 9 meters

• 7 meters

• 5 meters

A car's distance from a starting point can be modeled by the polynomial function d(t) = 4t^2 + 2t, where t is the time in hours. Solve for t when the car has traveled 50 meters.

• 4.0 hours

• 5.1 hours

• 2.5 hours

• 3.3 hours

A company's profit can be modeled by the polynomial P(x) = -2x^2 + 12x - 16, where x is the number of products sold. Determine the number of products sold that maximizes the profit by finding the vertex of the graph.

• 2

• 5

• 4

• 3

The volume of a cube can be represented by the polynomial V = x^3, where x is the length of a side. If the volume is 64 cubic meters, solve for x to find the length of a side of the cube.

• 2 meters

• 4 meters

• 8 meters

• 6 meters

A ball is thrown into the air, and its height in meters can be modeled by the polynomial function h(t) = -5t^2 + 20t + 2. Graph this function to find the maximum height of the ball.

• 25 meters

• 15 meters

• 18 meters

• 22 meters

The cost of producing x items is given by the polynomial C(x) = 3x^2 + 5x + 10. If the company wants to minimize costs, solve the polynomial equation to find the optimal number of items to produce.

• 10

• 0

• 5

• -3

A rectangular pool has a length that is twice its width. If the area of the pool is represented by the polynomial A = 2x^2, where x is the width, find the width of the pool by solving the polynomial equation.

• 2x

• x^2

• x

• 4x

The profit function for a product is given by P(x) = x^3 - 6x^2 + 9x. Graph this polynomial function to determine the intervals where the profit is positive.

• (-∞, 0)

• (0, 3) and (3, ∞)

• (3, 5)

• (5, ∞)

A farmer has a field in the shape of a rectangle. The length is represented by the polynomial L = 4x + 2, and the width is represented by W = 2x - 1. Find the area of the field by solving the polynomial equation for area A = L * W.

• 8x^2 - 2

• 4x^2 + 2x

• 10x^2 - 1

• 6x^2 + 3