MTH 163

 I already did the exploring the coefficient on Wolfram. So what I need is discovering a real life example, Expanding on your own real life example, and exploring one coefficient. So what you need to do is bascially using example at the last page and explaining it. you DON’T NEED Wolfram for the parts I need help with. If possible, please get it done by 10 pm tonight. Thank you. 

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 Demonstration
s
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 E
xample 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 Demonstration
s
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 words

using
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.