You will use P(x)
= −0.2x2 + bx – c where (−0.2x2 + 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
If your last name
begins with the letter
Choose a fixed
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) = −0.2x2 + bx − c. This is
your quadratic profit model function. State that quadratic profit model
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
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