Maximizing Harvest with Tree Planting

The video tutorial explains how a farmer can maximize fruit harvest by determining the optimal number of trees to plant per acre. It introduces a quadratic equation to model the relationship between the number of trees and the yield per tree. The tutorial demonstrates how to find the vertex of the parabola representing the equation to identify the optimal number of trees. The solution involves calculating the vertex using the formula for the x-coordinate and substituting it back into the equation to find the total harvest. The farmer should plant 57 trees per acre to achieve the maximum yield of 9,633 bushels.

What is the initial yield per tree if 95 trees are planted per acre?

• 50 bushels

• 55 bushels

• 60 bushels

• 65 bushels

How does the yield per tree change with each additional tree planted?

• Decreases by 5 bushels

• Increases by 3 bushels

• Decreases by 3 bushels

• Increases by 5 bushels

What is the expression for the total number of trees per acre?

• 95 + x

• 95 - x

• x - 95

• x + 55

What type of mathematical function represents the total harvest per acre?

• Linear function

• Logarithmic function

• Exponential function

• Quadratic function

What is the significance of the vertex in the context of this problem?

• It represents the total number of trees.

• It represents the minimum harvest.

• It represents the average harvest.

• It represents the maximum harvest.

How is the x-coordinate of the vertex calculated?

• Using the formula -b/2a

• Using the formula a/b

• Using the formula b/2a

• Using the formula -b/a

What is the optimal number of trees to plant per acre to maximize the harvest?

• 38 trees

• 57 trees

• 100 trees

• 95 trees

What is the total harvest per acre when the optimal number of trees is planted?

• 8,000 bushels

• 11,000 bushels

• 9,633 bushels

• 10,000 bushels

What does the y-coordinate of the vertex represent in this problem?

• The total harvest per acre

• The number of additional trees

• The total number of trees

• The yield per tree

Why is the x-coordinate of the vertex negative in this context?

• It indicates an error in calculation.

• It indicates no change in the number of trees.

• It indicates planting fewer than 95 trees.

• It indicates planting more than 95 trees.