MATH 133 Unit 2 – Individual Project Assignment – Quadratic Equations

MATH 133 Unit 2 – IndividuRemember that the
standard form for the quadratic function equation isy=f(x)
=ax2+bx+cand the
vertex form isy=f(x) =a(x–h)2+k,
where (h,k) are the coordinates of the vertex of this
quadratic function’s graph.

You will use P(x)
= ?0.2×2+ bx– cwhere (?0.2×2+ bx)
represents the business’ variable profit and cis 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:
3.
Replace band cwith
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.
4.
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.
5.
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.)
6.
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.
7.
What is the vertex of
the quadratic function graph? (Show your work details, or explain how you found
the vertex.)
8.
What is the equation of
the line of symmetry? Explain how you found this equation.
9.
Write the vertex form
for your quadratic profit function.
10.
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.
11.
How would knowing the
number of items sold that produces the maximum profit help you to run your
business more effectively.
12.
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 intellipathLearning
Nodes seemed to be most helpful in completing this assignment?
Suppose that you need to
fence a rectangular play area in your backyard for your child or pet. Further,
suppose that you know the length must be 8 feet longer than the width. The back
of your house will serve as one side of the fenced area.
Note:The perimeter (distance around) of a general
rectangle is P= 2L+ 2W, and its area
is A= Lx W. In this
situation, P= L+ 2W.

1. Based on the first
letter of your last name, choose a value for your backyard area that must be
fenced from the range corresponding to the first letter of your last name
indicated in the following table.l Project Assignment – Quadratic Equations