Question
Birthday Polynomial For this project you are going to create a polynomial whose x-intercepts are the digits in your birthday, from this format MM/DD/YY. Five
Birthday Polynomial
For this project you are going to create a polynomial whose x-intercepts are the digits in your birthday, from this format MM/DD/YY. Five of your digits will be used to create real x-intercepts. One of your digits must be used to create a complex x-intercept, meaning it will also have a complex pair. You will be creating a degree seventh polynomial.
In each part you will need to textually document your process. Your documentation should follow the structure below but does not need to do so rigidly. You will not receive credit for any superficial documentation.
I did _____________, because ______________.
Please note that because statements like, "because that is what you are supposed to do" will be considered superficial and not counted.
Part 1: Creating your Polynomial
In this part you will be creating the polynomial using the digits of your birthday. You may choose the x-intercepts to be positive or negative.
- Use the digits of your birthday to create the x-intercepts
- 5 of your digits must be used to create real x-intercepts
- 1 of your digits must be use to create complex x-intercepts
- Don't forget about the conjugate pair.
- Use the x-intercepts to create the factors of your polynomial.
- Distribute the factors so that your polynomial is in standard form
Part 2: Using Synthetic Division and Quadratic Solving techniques to find the factors.
Yes, I know you already know that the factors are because you created them in the first step. The purpose of this step is to show that you know how to use synthetic division to find factors, and be able to find complex factors once you have found all the real ones.
- Use the rational root theorem to find possible zeros.
- Use synthetic division to confirm which of the possible zeros are correct.
- Once you are down to a quadratic, find the remaining complex zeros.
Part 3: Graphing your polynomial
Now you need to graph your polynomial.
- Using the standard form, discover the degree of your polynomial, and thus plot your end behavior.
- Using your factors, plot your x-intercepts
- Using the exponents on your factors decide if your roots are crossing or non-crossing.
- Now, finish drawing the graph using this knowledge.
Part 4: Reflection
This is part you will reflect about this process. Your reflection needs to contain the following elements.
- At least one instant of difficulty
- At least one thing you tried to do to overcome that difficulty
- At least one that that surprised you
- At least one thing you would do differently, or one piece of advice for next year's students when they do this project.
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