My Birthday Polynomial     

In this project you will create a poster of a custom polynomial based on the digits from your birthday.  If your birthday was 9-6-1974 a possible polynomial might be:

birthdaypoly1

or

birthdaypoly2

 

Notice that the expression MUST use the digits of my birthday in order. However, you may use positive or negative numbers and ANY power of x on your polynomial. You may also choose to make a polynomial or rational expression.

  • Use www.desmos.com to design and test your function until its perfectly suited for you.
  • Use www.wolframalpha.com or GeoGebra to test your function and gather complex information!
  • Use Daum Equation editor in the app store or the built in equation editor in Google Docs (Insert -> Equation) to make your math look professional!

To Earn a 7 : The Basics

  • function
  • image from Desmos or graphing utility that shows real roots
  • ALL real and complex roots (function MUST have complex roots!)
  • asymptotes
  • domain and range
  • y- intercept
  • clear description of the function’s end-behavior

To Earn an 8: Complex Plane Analysis

  • All directions from the 7 above should be followed.
  • Use GeoGebra to plot your function on the Complex Plane.
  • Show the function
  • Real Zeros
  • Complex Zeros (For rational expressions only use the NUMERATOR for complex root analysis — why is this?)
  • Make note of any symmetries you see
  • Be sure to adjust the viewing window so ALL interesting parts of the function are shown
  • This should be VERY clear and colorful – Have fun with it!
  • Consider using a Google Slideshow to put all the pieces together

To Earn a 9: Data & Research

  • All directions from the 7 & 8 assignment above
  • Give the EXACT coordinates of 10 points on the graph.
  • Use 5 integer x – values (at least one negative)
  • Use 3 rational x – values
  • Use 2 irrational x – values
  • Use Wolfram Alpha to evaluate your function at a complex number and return the exact result
  • Optional : Show the Julia Set for your polynomial !

Project Notes:

Your final project should be a .pdf document created from a GDoc, Google Slide Presentation, etc.  You can do this by going to FILE -> Download as…. .pdf.

  • Be creative in the way you develop and present your final product
  • Have Multiple “snapshots” of your polynomial — A local photo, a global photo, a complex photo?   It could have a photo booth look to it!
  • Be colorful and make make something you will be PROUD to have in your portfolio
  • Organize your final presentation.  It should, in essence, be a ‘Poster’ that has all of the information.
  • Have FUN with it and make it a very personal document….it IS your birthday!

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