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Polynomial Analysis Project

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People often say that Math is the subject that brings stress and apprehension upon them. However, I feel that this substantial subject provides amazing thought and insight to our lives. Usually, Math isn’t a subject that requires you to write essays, but the Quartic Polynomial Analysis Project did. This method helped me to get a clear understanding and master the different concepts of quartic polynomials. Calculators usually hinder us, because we use them so often that we are stuck when they are taken away. Nevertheless, this project required me to provide detailed information of how I came up with my solution without the use of a calculator. Therefore, I have now learned to not be so dependent on one. Keep reading if you would like to be …show more content…
My first instruction was to find the end behavior. The end behavior of a polynomial function is the behavior of the graph as x approaches positive infinity or negative infinity. Using the calculator, I typed my function into the “Y=” and selected the “GRAPH” feature. While analyzing the graph, I noticed that both ends were pointing upward, so the end behavior of both, positive infinity and negative infinity, approached positive infinity. Now, I was required to put my calculator away. I used purplemath.com and khanacademy.com for help. I had to study the degree and the leading coefficient of my function, in order to find the end behavior. I learned that even degree polynomials end in the same direction. Last, I looked at the leading coefficient and noticed that it was positive. When the leading coefficient and degree are both positive, the end behavior will be positive on both …show more content…
A trick that I learned for finding the number of zeros a function has, is to look at the exponents. Whatever your highest exponent is, that is the maximum number of zeros that your function can have. Since my highest exponent was four, my function, at most, has four zeros. There could be less, but never more than whatever the highest exponent is. I used the Descartes Rule of Sign to help me determine how many zeros were positive or negative. First, you have to count the number of changes in sign, when a number went from positive to negative or negative to positive, throughout the function. I counted a total of two positive zeros. To find the amount of negative zeros, you must change f(x) to f(-x), and repeat the positive steps. I came up with a total of two negative zeros. Lastly, I needed to find out what my exact zeros were. I used the rational theorem to find all og my possible zeros. The rational theorem requires you to focus on the factors of the degree and leading coefficient. My possible zeros were (plus or minus for all) 1, ½, ¼, 2, 4. Since I knew that I could only have four exact zeros, I had to use synthetic division, using 2 and -2, to eliminate the unwanted zeros. The exact zeros that I came up with were 2, -2, ½, and

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