Exam 2 Project – Chs. 2 & 3 Exploring Quadratic FunctionsAs a .docx

Exam 2 Project – Chs. 2 & 3: Exploring Quadratic Functions
As a review, it is recommended that you complete & submit this
assignment before taking the exam.
Due Date: The original post is due by 11:59pm three (3) days
before Exam 2 is due. Replies are due by 11:59pm of the last
day that Exam 2 is due.
Introduction
Project:
Graphs represent many situations in life. Look at the first page
of each section of your text and you will see “What you should
learn” and “Why you should learn it”. These short paragraphs
describe real life problems that relate to the math in the section.
Scan through the book, look for pictures of real life examples
and write down several examples that seem interesting to you.
For this project, you will learn how coefficients in a quadratic
function affect the graph of the function by using Wolfram
Demonstrations Project website
(http://demonstrations.wolfram.com/). You will then analyze a
quadratic and describe a quadratic function that models a real
life situation from a graph that corresponds to the data. We will
guide you through the process first. You will then have the
opportunity to get creative, so prepare to impress.
Note: Points will not be deducted for how precisely the equation
matches the real life situation.
Activity/Process and Grading (Total = 50 (40 + 5 + 5) points)
Complete all of the following activities using Wolfram
Demonstrations Project website (http://www.wolfram.com/).
You will submit your work to Exam 2 Project forum in
Blackboard. Only submit your work in one of the following
ways:Take a picture of your written project. Make sure it is

readable. Upload the image to the discussion forum.
Use Word and an equation editor to type your project. Make
sure you answer all questions in complete sentences.Upload the
file to the discussion forum.To snip/crop & copy an image, pull
up your image/photo on the screen:Mac: Use Command + Shift
+ 4, click and drag cursor across the part of the image that you
want to use. It will take a screenshot of your selected area and
automatically save it to your desktop.Windows: Go to Start
Menu>>All Programs>>Accessories>>Snipping Tool. Drag the
cursor around the area that you want to capture. Name and save
to your desktop.
This assignment is REQUIRED and will only be graded if
resources and conclusion are part of the project. The point
values for each section are noted below with an additional 10
points for replies to classmates. You are required to review at
least two classmates’ projects and post a substantive reply to
each (5 points for each reply for up to a total of 10 points).
“Good Job” or “I didn’t think of that” will not do. You must
post a follow-up question, an observation, make a suggestion, or
apply some additional insight to what your classmate has
posted. It is NOT your place to point out or correct errors. If
you find an error that needs correcting, email your instructor for
verification and the instructor will contact the student if your
observation is correct.
To get started:
Review the Example below at the bottom of this document.Click
on the hyperlink Wolfram website (http://www.wolfram.com/).
Click on the “Try the Interactive CDF examples” link under
Professional & Enterprise column on the left of the page

(http://www.wolfram.com/cdf/uses-examples/?fp=left). Note:
You may need to download the CDF player first. Scroll to the
middle of the page & click on the red “Interact Now: Get the
free Wolfram CDF Player” button.On the CDF Player page
(http://www.wolfram.com/cdf-player/ or
http://www.wolfram.com/cdf-
player/plugin/success.html?platform=WIN), click on “Explore
demonstrations now” link at the bottom left of the page. Under
the heading Wolfram Demonstrations Project, search for
parabolas and choose the following demonstration: How does
the vertex location of a parabola change?
Exploring the coefficients: 5 points
Using the application, click on LABEL and GRID to see the
equation and a grid. Move the sliding bar for the c variable to
the left and right. For this project, use the title “C-variable”
and describe what happens to the parabola and the equation.
Please write your description in complete sentences. Reset the
parabola and investigate further by changing the ‘a’ and ‘b’
variables. The use the title “A-variable” and “B-variable” and
describe how the variables affect the graph of the parabola.
Discovering a real life example: 15 points
Recall the definition of a function. View the real life example
at the end of the project and answer the questions that will help
describe the function with as much detail as possible.
You will be graphing the function, finding the maximum
(vertex) point, determining the domain, finding random points
and writing them using functional notation and determining
where the function is increasing and decreasing.
Expanding on your own real life example:15 points
Review the introduction and the examples you wrote down from
within the textbook. Write a real life description of what a
function could represent (Review the Example below at the

bottom of this document). Include descriptions of each piece
found In the example below. Will your real life example be a
function that represents the height of a punted football, the path
of a kid as he dives off a diving board, a function describing the
number of dates 18-year-olds go on or one describing the
number of IPhones purchased between two different years? You
decide and be creative!
Consider restricting the domain so that the function is valid for
your description.
For the important parts of a parabolic function discussed above
(vertex, domain, etc.) describe in your own wordsusing non-
math terms what each of these parts represent in the real world.
Exploring one coefficient change: 5 points
Change a constant or coefficient in the problem so that the
function has imaginary solutions.
Show algebraically how to obtain the solutions.
Answer the question: Can these solutions be graphed? Can
they help understand the real world?
CONCLUSION & RESOURCES
Write a summary (minimum of 3 sentences) of what you learned
doing this project.
Remember to list any resources you used for this project
including books and or internet sites.

Example
A biker traveling with a velocity of 80 feet per second leaves a
100 feet platform and is projected directly upward. The
function for the projectile motion
Is s(t) = -16t2 +80t + 100 where s(t) is the height and t is the
seconds the biker is in the air.
Draw a rectangular coordinate system and sketch the height of
the biker after the bike leaves the platform. Make the
horizontal axis the time the biker is in the air. Label the
horizontal and vertical axes. Don’t forget that the biker leaves
the platform at 100 feet.
Use your graphing utility to graph the parabola.
Using your graphing calculator, find how many seconds it takes
for the biker to reach its maximum height. Compare this value
to –b/2a, where a and b are the coefficients found from
comparing the form
f(x) = ax2 + bx + c to the given quadratic function. This value,
–b/2a, is the x-value of the vertex. Find the y-value at this
point by evaluating the function at the x-value of –b/2a. What
does the y-value represent at this specific x-value? Then state
the (x, y) point of the vertex or maximum point.Looking at your
calculator, find the number of seconds the biker is in the air (or
“hang time”). Then find the range of height values that the
biker attains. State the domain and range of this real life
example. Remember that time isn’t negative and that the model
is valid only when the biker is in the air! Use the graph to
determine when the biker will reach a height of 100 feet. State
the (these) point(s) as an order pair and using functional
notation.Use the graph to determine what height the biker will
attain after 1 second. State the point as an ordered pair and
using functional notation.
Where is the function increasing? In other words, for what x-

values does the biker continue to get higher? Where is the
function decreasing? In other words, for what x-values does the
biker start descending toward the ground? State these intervals
using interval notation.
Fore Prob 1This assignment is for the Winter 2015 class only
and NOT to be shared with anyone outside of this section.
Forecasting Problem 1 (10 points)The following equation
summarizes the trend portion of quarterly sales of automatic
dishwashers over a long cycle. Sales also exhibit seasonal
variations. Ft = 40 - 6.5t + 2t2 whereFt = Unit sales (in 000
units)t = 1 at the first quarter of
2010QuarterRelative111021003604130a) Using the
information given, prepare a seasonalized forecast of sales for
each quarter of 2014.b) Prepare a quarter-by-quarter time
series plot showing the forecast trend (seasonally unadjusted
forecast) from the first quarter of 2010 to the fourth quarter of
2014. Superimpose on this graph the seasonally adjusted
forecast for the same time period.
Forecasting Problem 2 (10 points)The data below represent the
relative shares (by quarter) of call volumes over 16 quarters
from a call center at a major financial institution.
2010201120122013Average Qtr Percent Share
Q123.2%23.0%23.3%21.9%22.8%Q225.1%24.6%26.2%25.3%2
5.3%Q328.5%28.8%28.6%29.8%28.9%Q423.2%23.6%21.9%23.
1%22.9%Total100%100%100%100%100%(a) Using the average
quarter percent share column (Column G), generate a pie chart
and a bar chart to show the quarterly percent shares of call
volumes to the call center.(b) Using the percentage table above,
what are the indices for each of the four quarters?(c) Assume
that the projected number of calls for the year 2014 is
50,000,000, what are the seasonally adjusted forecasts for the

number of calls for Q1, Q2, Q3, and Q4?
Forecasting Problem 3 (15 points)The data below represent the
call volumes over 16 quarters from a call center at a major
financial institution. Develop a forecasting model for the
volume of calls (in 000
units).2010201120122013YearQuarterDemandMA(4)MA(2)
Demand/MA(2)Deseas.
DemandQ147354462870920101473483.80Q25135827077252513
504.32Q35826817738543582510.5519.381.12516.41Q44745575
926614474528.25536.880.88542.9320111544545.5557.880.9855
6.422582570.25580.631.00572.15(a) Create a time series graph
showing the: (1) actual data, (2) trend line for the data, and (3)
deseasonalized actual data. Label the graph
appropriately.3681591601.501.13604.264557612627.630.89638.
0020121628643.25654.750.96642.342707666.25670.631.05695.
043773675685.131.13685.89(b) Develop the quarterly (Q1, Q2,
Q3, Q4) indexes for the volume of
calls4592695.25697.500.85678.09See page117-118 of text for
similar
problem20131709699.75709.881.00725.192725720728.631.0064
3.303854737.25757.764661757.13(c ) Using the trend line you
developed in Part (a), what are your seasonally unadjusted and
seasonally adjusted forecasts for the four quarters of
2014?YearQuarter
Relatives2010201120122013Q10.980.961.000.98Q21.001.051.0
01.02Q31.121.131.131.13Q40.880.890.850.87
Deseasonalized Demand 483.7982252074457 504.32006982339
516.4139696404509 542.9335152668235
556.4191004500009 572.1525938347231
604.2575830328987 638.0041519063728
642.3367556665451 695.037601101631
685.8900318420421 678.094179404978
725.1859231967843 643.2991889850977
757.7620791631358 757.1288050450851 Actual Demand

473.0 513.0 582.0 474.0 544.0 582.0
681.0 557.0 628.0 707.0 773.0 592.0
709.0 725.0 854.0 661.0
Forecasting Problem 4 (15 points)Many supply managers use a
monthly reported survey result known as the purchasing
managers’ index (PMI) as a leading indicator to forecast future
sales for their businesses. Suppose that the PMI and your
business sales data for the last 10 months are the
following:12345678910MonthPM4343.141.538.540.545.246.248
.14953Sales (in $000)122124125123119120125127135136A.
Develop a regression model that can be used by supply
managers in forecasting future sales for businesses. Explain
what forecasting model approach you used and why you chose
it. Show complete work (cut and paste from Excel if used in the
analysis). (10 points)B. Develop a sales forecast for the 11th
and 12th months using the model you developed in part A when
PMIs are 52 and 50, respectively. (10 points)
Fore Prob5Forecasting Problem 5 (15 pts)An electrical
contractor's records during the last 5 weeks indicate the number
of job requests:F1F2WeekActual RequestsNaïve2-
MaMADMSEMAPE120WeekActualF1F2F1F2F1F2F1F2222203
1822214.001.0016.001.0022.22%5.56%318222142118203.002.0
09.004.0014.29%9.52%42118205222119.51.001.501.002.254.55
%6.82%5222119.52.71.58.72.413.7%7.3%62221.5a)Graph the
actual request data using appropriate labels, and provide
insights about the time series (describe what you observe re the
behavior of the sales over the period under review).b)What is
the forecast for Week 6 using a 2-period moving average?c)
What is the forecast for Week 6 using the Naïve
method?Compute the MAD, MAPE, and MSE for the two-period

moving average and Naïve models and compare your results.
Explain which of the two forecasting models you prefer and
why.d)e)Graph the actual number of requests, the 2-period and
Naïve forecasts. Use appropriate labels for your graphs
Rel Prob 1Reliability Problem 1 (15 points)One of the industrial
robots designed by a leading producer of servomechanisms has
three major components. Components’ reliabilities are 80, 85,
and 95%. All of the components must function in order for the
robot to operate effectively.a. Compute the reliability of the
robot.b. Designers want to improve the reliability by adding a
backup component. Due to space limitations, only one backup
can be added. The backup for any component will have the same
reliability as the unit for which it is the backup. Which
component should get the backup in order to achieve the highest
reliability? Show proof of your answer by computing the overall
reliabilities of the three options (assume 100% reliable backup
switch)c. If one backup with a reliability of 99% can be added
to any of the main components, which component should get it
to obtain the highest overall reliability? Show proof of your
choice by computing the overall reliabilities of the three options
(assume a backup switch with 100% reliability).
Rel Prob 2This assignment is for the Winter 2015 class only and
NOT to be shared with anyone outside of this section.
Reliability Problem 2 (10 points)Lucky Lumen light bulbs have
an expected life that is exponentially distributed with a mean of
20,000 hours. Determine the probability that one of these light
bulbs will last:a. At least 24,000 hoursb. No longer than
4,000 housc. Between 4,000 and 24,000 hours
Rel Prob 3This assignment is for the Winter 2015 only and
Reliability Problem 3 (10 points)An office manager has
received a report from a consultant that includes a section on
equipment replacement. The report indicates that scanners have
a service life that is normally distributed with a mean of 41
months and a standard deviation of 4 months.On the basis of
this information, determine the percentage of scanners that can

be expected to fail in the following time periods.a. Before 38
months of service.b. Between 40 and 45 months of service.c.
Within +/- 2 months of service.d. If the manufacturer of the
scanner offers a service contracts of 3 years on these scanners,
what percentage of scanners can be expected to fail from wear-
out during the service period?e. If the cost of replacement
each scanner is $250, and if 1,000 units of this scanner are sold,
what is the expected warranty replacement cost to the
manufacturer.
Rel Prob 4This assignment is for the Winter 2015 class only and
Reliability Problem 4 (10 points)How high must reliability be?
Prime business customers expect public carrier-class
communications data links to be available 99.999 percent of the
time. The so-called five nines rule implies only 5 minutes of
downtime per year. Such high reliability is needed not only in
telecommunications but also for mission-critical systems such
as airline reservation systems or banking fund transfers.Suppose
a certain network web server is up only 90 percent of the time
(i.e. its probability of being down is 0.10). How many
independent servers are needed to ensure that the system is up
at least 99.999 percent of the time? Show your work and explain
your answer.

Exam 2 Project – Chs. 2 & 3 Exploring Quadratic FunctionsAs a .docx

Recommandé

Recommandé

Contenu connexe

Similaire à Exam 2 Project – Chs. 2 & 3 Exploring Quadratic FunctionsAs a .docx

Similaire à Exam 2 Project – Chs. 2 & 3 Exploring Quadratic FunctionsAs a .docx (12)

Plus de gitagrimston

Plus de gitagrimston (20)

Dernier

Dernier (20)

Exam 2 Project – Chs. 2 & 3 Exploring Quadratic FunctionsAs a .docx