This document summarizes how changing the coefficients (a, b, and c) of a quadratic function affects its graph. It describes how moving the c-variable left and right changes the parabola's position, and how changing the a- and b-variables affects the shape and orientation of the parabola. It then analyzes a real-life example of a biker projected upward from a platform to find properties like the vertex, domain and range, and intervals of increase/decrease.

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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

4. 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).

5. “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

6. 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.

7. 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

8. 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.
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12. INFORMATION GATHERING: INTERACTIVE METHODS
3. Ever since you walked through the door, your interviewee,
Max Hugo, has been shuffling
papers, looking at his watch, and drumming on his desk with his
fingers, Based on what you
know about interviews, you guess that Max is nervous because
of the other work he needs to
do. In a paragraph, describe how you would deal with this
situation so that the interview can be
accomplished with Max's full attention. (Max cannot reschedule
the interview for a different
dav')
4. Write a series of six closed qlestions that cover the subject of
decision-making style for the manager
described in Problem 2.
5. Write a series of six open-ended questions that cover the
subject of decision-making style for the
manager described in Problem 2.
6. Examine the interview structure presented in the sequencing
of the following questions:
1. How long have you been in this position?
2. What are your key responsibilities?
3. What reports do you receive?
4. How do you view the goals of your department?

13. 5. How would you describe your decision-making process?
6. How can that process best be supported?
7. How frequently do you make those decisions?
8. Who is consulted when you make a decision?
9. What is the one decision you make that is essential to
departmental functioning?
a. What structure is being used? How can you tell?
b. Restructure the interview by changing the sequence of the
questions (you may omit some, if
necessary). Label the reordered questions with the name of the
structure you have used.
7. The following is the first interview report f,led by one of
your systems analysis team members: "In
my opinion, the interview went very well. The subject allowed
me to talk with him for an hour and a
half. He told me the whole history of the business, which was
very interesting. The subject also men-
tioned that things have not changed all that much since he has
been with the flrm, which is about 16
years. We are meeting again soon to finish the interview
because we did not have time to go into the
questions I prepared."
a. In two paragraphs, critidue the interview report. What critical
information is missing?
b. What information is extraneous to the interview report?
c. If what is reported actually occurred, what three suggestions
do you have to help your teammate

14. conduct a better interview next time?
8. Cab Wheeler is a newly hired systems analyst with your
group. Cab has always felt that question-
naires are a waste. Now that you will be doing a systems project
for MegaTrucks, Inc., a national
trucking firm with branches and employees in 130 cities, you
want to use a questionnaire to elicit
some opinions about the current and proposed systems.
a. Based on what you know about Cab and MegaTrucks, list
three persuasive reasons why he should
use a survey for this study.
b. Given your careful arguments, Cab has agreed to use a
questionnaire but strongly urges that
all questions be open-ended so as not to constrain the
respondents. In a paragraph, persuade
Cab that closed questions are useful as well. Be sure to point
out trade-offs involved with each
question type,
9. "Every time we get consultants in here, they pass out some
goofy questionnaire that has no mean-
ing to us at all. Why don't they bother to personalize it, at least
a little?" asks Ray Dient, head of
emergency systems. You are discussing the possibility of
beginning a systems project with Pohattan
Power Company (PPC) of Far Meltway, New Jersey.

15. a. What steps will you follow to customize a standardized
questionnaire?
b. What are the advantages of adapting a questionnaire to a
particular organization? What are the
disadvantages?
10. A sample question from the draft of the Pohattan Power
Company questionnaire reads:
I have been with the company:
2G-upwards years
10-15 years upwards
5-10 years upwards
less than a year
Check one that most apPtes.
a. What kind of a scale is the question's author using?
b. What errors have been made in the construction of the
question, and what might be the possible
responses?
c. Rewrite the question to achieve clearer results.
d. Where should the question you've written appear on the
questionnaire?