MATH133 UNIT 2 Quadratic Equations Individual Project Assignm.docxhealdkathaleen
MATH133 UNIT 2: Quadratic Equations
Individual Project Assignment: Version 2A
Show all of your work details for these calculations. Please review this Web site to see how to type mathematics using the keyboard symbols.
Problem 1: Modeling Profit for a Business
IMPORTANT: See Question 3 below for special IP instructions. This is mandatory.
Remember that the standard form for the quadratic function equation is
y
=
f
(
x
) =
ax
2
+
bx
+
c
and the vertex form is
y
=
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
x
2
+
bx
–
c
where (−0.2
x
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
4.Replace
b
and
c
with your chosen values in Parts 1 and 2 in
P
(
x
) = −0.2
x
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 cal.
MATH133 UNIT 2 Quadratic Equations Individual Project Assignm.docxhealdkathaleen
MATH133 UNIT 2: Quadratic Equations
Individual Project Assignment: Version 2A
Show all of your work details for these calculations. Please review this Web site to see how to type mathematics using the keyboard symbols.
Problem 1: Modeling Profit for a Business
IMPORTANT: See Question 3 below for special IP instructions. This is mandatory.
Remember that the standard form for the quadratic function equation is
y
=
f
(
x
) =
ax
2
+
bx
+
c
and the vertex form is
y
=
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
x
2
+
bx
–
c
where (−0.2
x
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
4.Replace
b
and
c
with your chosen values in Parts 1 and 2 in
P
(
x
) = −0.2
x
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 cal.
MATH133 UNIT 2 Quadratic EquationsIndividual Project Assignment.docxandreecapon
MATH133 UNIT 2: Quadratic Equations
Individual Project Assignment: Version 2A
Name (Required): __________________________________________________
Show all of your work details for these calculations. Please review this Web site to see how to type mathematics using the keyboard symbols. Handwritten scanned work is not acceptable for AIU Online.
Problem 1: Modeling Profit for a Business
IMPORTANT: See Question 3 below. This is mandatory.
Remember that the standard form for the quadratic function equation is y = f (x) = ax2 + bx + c and the vertex form is y = 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) = -0.2x2 + bx – c where (-0.2x2 + bx) represents the business’s 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. (List your chosen value for between 100 and 200.)
2. (List what the fixed costs might represent for your fictitious business, and be creative; also list your chosen value for c from the table below).
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
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. (State that quadratic profit model function’s equation by replacing and with your chosen values.)
5. (Choose five values of (number of items sold) between 500 and 1000. Insert those -values in the table.)
6. Plug these five values into your model for and evaluate the annual business profit given those sales volumes. (Be sure to show all your work for these calculations; complete the table below.)
7. Use the five 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 a quadratic function is called aparabola. (Insert graph below.)
8. (Show work details or explain how you found the vertex. Write the vertex in ordered-pair form: .)
9. (Write the explanation and the equation of the line of symmetry.)
10. (Write your quadratic profit function in vertex form, where is the vertex of this quadratic function’s graph. Show the details of how you found this equation.)
11. (State the maximum profit (if any), and show how you determined how many items must be sold to give the maximum profit.)
12. (State how knowing the number of items sold that produces the maximum profit help you to run business more effectively.)
13. (Give an analysis of the results of these profit calculations, and give some ...
Page 1 of 3 MATH133 Unit 4 Functions and Their Graphs .docxalfred4lewis58146
Page 1 of 3
MATH133 Unit 4: Functions and Their Graphs
Individual Project Assignment: Version 2A
IMPORTANT: Please see Question 3 under Problem 2 for special instructions for this
week’s IP assignment. This is mandatory.
Show all of your work details, explanations, and answers on the Unit 4 IP Answer Form
provided.
Problem 1: Children’s Growth
A study of the data representing the approximate average heights of children from birth to 12
years (144 months) has shown the following two equations. The function is the radical
function representing the girls’ heights in inches after x months, and the function is the radical
function representing the boys’ heights in inches after x months ( months).
( ) √
( ) √
1. Choose five different values of x between 0 and 144 months, and calculate the values of each of
these functions for the chosen x values. Show all of your work and display these calculated values
of ( ) and ( ) in “t-tables” in the Answer Form supplied.
2. Use these five different values of x and the corresponding calculated values of both functions,
together with Excel or another graphing utility, to draw the graphs of these two functions. These
graphs should be drawn on the same coordinate system so that the two functions can be easily
compared. Insert those graphs into the Answer Form.
3. Set the two functions equal to each other, and solve the resulting radical equation for x. This
value of x will be the age in months when boys and girls are the same height. (Show all of the
steps for solving this radical equation on the Answer Form provided.)
4. What is the height in inches when boys and girls (according to these radical functions) are the
same height? (Show all of your work on the Answer Form provided.)
5. Based on each of the two radical functions above, what is the average change in height per
month for girls and the average change in height per month for boys between the two values of
x (x = 30 months and x = 60 months)? (Show all of your work on the Answer Form provided.)
Page 2 of 3
6. Describe the transformations of the radical function ( ) √ that will result in each of these
functions.
7. Which intellipath Learning Nodes helped you with this problem?
Problem 2: Average Cost
Your company is making a product item. The fixed costs for making this product are b, and the variable
costs are mx, where x is the number of items produced. The cost function is the following linear function:
( )
The average cost is the total costs divided by the number of items produced, which is a rational function,
as follows:
̅
1. Based on the first letter of your last name, choose values for m and b from the following tables
(Neither m nor b has to be a whole number):
First letter of your last name Possible values for m
A–F $10–$19
G–L $20–$29
M–R $30–$39
S–Z $40–$49
First letter of .
What is four times three? 12 you might say, but no longer! In a new type of math— intersection math—
we will see that four times three is 18, two times two is 1, and that two times five is 10 (Hang on! That’s
not new!) Let’s spend some time together exploring this new math and answering the question: What is
1001 times 492?
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Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
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