Respond to the Following Questions Related to Algebra

M You will use P(x) = −0.2×2 + bx – c where (−0.2×2 + bx) represents the business’ variable profit and c is the business’s fixed costs. So, P(x) is the store’s total annual profit (in $1,000) based on the number of items sold, x. 1. Choose a value between 100 and 200 for b. That value does not have to be a whole number. 2. Think about and list what the fixed costs might represent for your fictitious business (be creative). Start by choosing a fixed cost, c, between $5,000 and $10,000, according to the first letter of your last name from the values listed in the following chart: If your last name begins with the letter Choose a fixed cost between A–E $5,000–$5,700 F–I $5,800–$6,400 J–L $6,500–$7,100 M–O $7,200–$7,800 P–R $7,800–$8,500 S–T $8,600–$9,200 U–Z $9,300–$10,000 Page 2 of 4 3. Important: By Wednesday night at midnight, submit a Word document with only your name and your chosen values for b and c above in Parts 1 and 2. Submit this in the Unit 2 IP submissions area. This submitted Word document will be used to determine the Last Day of Attendance for government reporting purposes. 4. Replace b and c with your chosen values in Parts 1 and 2 in P(x) = −0.2×2 + bx − c. This is your quadratic profit model function. State that quadratic profit model functions equation. 5. Next, choose 5 values of x (number of items sold) between 500 and 1,000. Think about the general characteristics of quadratic function graphs (parabolas) to help you with choosing these 5 values of x. 6. Plug these 5 values into your model for P(x), and evaluate the annual business profit given those sales volumes. (Be sure to show all of your work for these calculations.) 7. Use the 5 ordered pairs of numbers from 5 and 6 and Excel or another graphing utility to graph your quadratic profit model, and insert the graph into your Word answer document. The graph of the quadratic function is called a parabola. 8. What is the vertex of the quadratic function graph? (Show your work details, or explain how you found the vertex.) 9. What is the equation of the line of symmetry? Explain how you found this equation. 10. Write the vertex form for your quadratic profit function. 11. Is there a maximum profit for your business? If so, how many items must be sold to produce the maximum profit, and what is that maximum profit? If your quadratic profit function has a maximum, show your work or explain how the maximum profit figure was obtained. 12. How would knowing the number of items sold that produces the maximum profit help you to run your business more effectively. 13. Analyze the results of these profit calculations and give some specific examples of how these calculations could influence your business decisions. 14. Which of the intellipath Learning Nodes seemed to be most helpful in completing this assignment?

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