Having taught his algebra students to solve linear-quadratic systems of equations graphically, Mr. Peters is preparing a lesson to show them how to use the table feature on a graphing calculator to generate the tables of values for given functions. First, the students will graph y = x² - 1 and generate the table of values. Then, the students will graph a particular linear equation in the same window and compare its table of values to that of the parabola. Mr. Peters wants to use a linear equation that will permit students to recognize that linear-quadratic systems can have more than one solution and to easily compare the graphical and tabular forms. Which of the following linear equations best supports his goals?

The data in the table shows the number of mother-to-child HIV infections diagnosed in the United States in various years from 1985 to 2005. How can we learn from the data? Practice the following questions: 1. Make a scatter plot to display the data. You can use any graphing technology. Why would a quadratic model make sense? 2. Determine an equation for this relation. Which form (standard, vertex or factored) do you think is the best for these data and why? 3. Based on your model, will the number of HIV cases ever be reduced to zero? If so, when? Explain reasoning.

The owner of an apartment building has 100 apartments. He has found that if he charges $500 per month he can rent all 100 of them but he rents one fewer apartment for each $25 increase in monthly rent.   a. Write an equation that gives the monthly revenue from the rental of the apartments if he makes x increases of $25 in the rent. b. Find the rent he should charge to maximize the monthly revenue and the number of apartments he will rent by charging this amount. c. Suppose the landlord pays for water, sewer, and electricity at his apartments for a cost of $50 per apartment per month. Write an equation that gives the monthly cost to the landlord after x price increases of $25. d. Write an equation that gives the monthly profit the landlord makes, and the rent he should charge to maximize his monthly profit, and the number of apartments he will rent by charging this amount. e. Explain why you know mathematically your solutions to (2) and (4) are maximum values. f. In a sentence or two…

Find the equation of the line parallel to the graph of 4x-5y=20 that has an x - intercept of 3