Maximizing the Area of a Corral

The video tutorial explains how to maximize the area of a corral with a cliff on one side, requiring fencing on only three sides. Using 1,200 yards of fencing, the tutorial derives a quadratic function to represent the area and finds the vertex to determine the dimensions that maximize the area. The maximum area is calculated and verified graphically using a graphing calculator.

What is the main objective when maximizing the area of the corral?

• To minimize the cost of fencing

• To maximize the area with limited fencing

• To ensure the corral is a perfect square

• To use all available fencing on all four sides

Why is one side of the corral not fenced?

• It is too expensive to fence

• It is a natural barrier like a cliff

• It is already fenced by the neighbor

• It is not necessary for the design

What variable is used to represent the length of the sides parallel to the cliff?

• X

• Z

• Y

• W

How is the length of the side perpendicular to the cliff expressed?

• 2X - 1,200

• X - 1,200

• 1,200 - X

• 1,200 - 2X

What type of function is used to model the area of the corral?

• Logarithmic function

• Quadratic function

• Exponential function

• Linear function

What is the formula for the x-coordinate of the vertex in a quadratic function?

• -B divided by 2A

• B divided by 2A

• A divided by 2B

• -A divided by 2B

What are the dimensions of the rectangle that maximize the area?

• 300 yards by 600 yards

• 400 yards by 800 yards

• 500 yards by 700 yards

• 200 yards by 900 yards

What is the maximum area of the corral?

• 160,000 square yards

• 180,000 square yards

• 200,000 square yards

• 150,000 square yards

How can the results be verified graphically?

• By drawing a sketch

• By using a graphing calculator

• By calculating manually

• By using a spreadsheet

What does the x-coordinate of the vertex represent in this context?

• The length of the corral

• The height of the corral

• The depth of the corral

• The width of the corral