1. What are four different methods for finding the roots of a function? Compare the methods. How do you know which method to use for a problem?

2. What are the conic sections? Where are they found in nature? The equations for the various conic sections are very similar. What set of rules might you use to determine which conic section is represented by a given equation?

3. People feel that they rarely use algebra in their jobs or their lives. Most feel that knowledge of simple arithmetic operations is all that is needed. If this is the case then why do you suppose that Algebra is a __required course__ in most college curriculums?

4. Please work on the following exercise. You may post your solution directly onto the body text of your message or use an attachment.

One side of a rectangular backyard is **2** meters longer than the other. If the diagonal is **10 **meters, then what are the lengths of the sides?

5. A Boeing 747 takes 30 minutes longer to fly from Denver, CO to San Francisco, CA than it takes to fly to Denver (a distance of 1200 miles). If the wind speed, from west to east, is 50 mph at cruise altitude, what is the speed of the airplane with no wind?

6. “What is the significance of the vertex of the parabolic graph? How would you use this concept in your workplace or real life?”

7. I look forward to your substantive discussion and your complete answer with examples. You may use your textbook or the findings of your own research on the Internet (e.g., *scholar.google.com*), etc., but you must provide proper citation and references.

8. Stephanie, the Team Manager of a soccer team purchases many soccer balls from a retailer and sells them to all the players at her soccer club at a price of **x** dollars each. She can sell **600 – 15x** balls per week.

**a) **Find a polynomial that represents the weekly revenue for the balls.

**b) **Find the revenue for a week in which the price is **$12** per ball. Use the parabolic graph to illustrate the law of diminishing return, if it occurs in this case. In order for Stephanie to receive the maximum weekly revenue,

**c) **How would you, as Business Manager, recommend for the price per ball?

150 Words per Question