Finding Maximum and Minimum Values by Completing the Square

This lesson teaches how to find maximum and minimum values of real-world functions by completing the square. It covers quadratic functions in vertex form, explaining how to identify vertices and determine if they represent maximum or minimum values. The lesson includes examples of maximizing revenue and minimizing production costs, demonstrating the application of these concepts in practical scenarios.

What does the vertex form of a quadratic function help you identify quickly?

• The slope of the function

• The vertex and whether it is a maximum or minimum

• The roots of the function

• The y-intercept of the function

In the revenue maximization example, what is the significance of the vertex (500, 500,000)?

• It is the point where revenue equals cost.

• It indicates the number of items to produce for maximum revenue.

• It represents the minimum revenue achievable.

• It shows the break-even point for production.

How do you confirm that 500 items produce the maximum revenue in the given example?

• By checking the revenue for 499 and 501 items and finding it lower

• By calculating the derivative of the function

• By graphing the function and observing the peak

• By comparing with industry standards

In the cost minimization example, what does the vertex (100, 2,200) represent?

• The optimal number of widgets for minimal cost

• The break-even point for production

• The maximum cost of production

• The average cost of production

What is the role of 'a' in determining the nature of the vertex in a quadratic function?

• It changes the symmetry of the graph

• It affects the horizontal shift of the graph

• It determines the y-intercept of the function

• It indicates whether the vertex is a maximum or minimum