*My Birthday Polynomial*** **

*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:**

or

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!