Final Algebra 2 Exhibition
Polynomials & Art Project Reflection
For AHS' 2015 All-School Math Exhibition, I exhibited my "Polynomials & Art" project from second semester. The Polynomials & Art project introduced our Algebra 2 class to the world of polynomials and quadratics by combining photography and functions with the recreation of lines and drawings from plotted points. The Polynomials and Art project required students to use polynomial functions to recreate lines in a picture and graph these functions in a way that could be turned into an interpretive art piece. The importance of this project lies in the understanding of polynomial functions, and how we can interpret these functions to find specific equations for lines in a picture.
The Polynomials & Art Project reflects our Algebra 2 class' knowledge of polynomials and graphing functions in the context of art and photographs. By learning more about the process of graphing and factoring functions through visualization, I was able to understand these concepts more easily, and I believe the rest of my class was as well. A large component of this project relied on using graphing calculators to determine local + global minimums and maximums, as well as determining accurate x-intercepts and scalars. By using this technology, our class was able to become more proficient using graphing calculators as well as doing these equations in writing as shown by the writing portion of this project.
When graphing polynomials, the “zeros” are a common term referring to the x-intercepts of the equation. The number of zeros can often be taken from the highest degree of a polynomial equation. For example, the equation F(x)=x3+2x2+4x would have 3 zeros since the highest degree is 3. To find a zero, there are two methods that one can use. The first method is factoring a polynomial into its simplest terms, and then using the zero product property to calculate the specified amount of zeros. The second method one can use it to factor the constant term into its positive and negative whole number factors. Once the factors have been identified, one can plug these negative and positive values in one by one to the original polynomial equation until the equation equals zero. Learning these two methods was very helpful in teaching me about algebraic equations as well as giving me a more in-depth understanding of quadratics.
During this project I learned that working with visual aspects really benefitted me as a learner. By taking a photograph and visualizing the lines I was going to graph, I was able to translate these lines onto paper much easier. This project made me feel comfortable with the the field of polynomials, and I am happy about how my final project came out. My biggest takeaway from this project was the skill of overcoming hard detail work and learning how to use scalars to find a “best fit” equation for a line. By learning these two skills, I’m sure that work in future math projects involving quadratics will be much easier. If I were to do this project over again, I would try to pick a picture that had 3 possible polynomial lines rather than two, so that I could get extra practice graphing and writing equations in this form.
If I were going to exhibit my project again, I would fix the title and my name on the board as well as add some interactive elements. My title and name could have used a little bit of refinement, and in hindsight I would have liked to print them out on a piece of paper and glue them on so that they would look more professional. As far as adding an interactive element, I would have liked to include my calculator and show people example functions on the screen so that they could understand the concept more completely. My greatest strength moving into future math classes is my will to learn and make mistakes. I know that there is still a lot that I have to learn in regards to math before I go to college, and I will use this understanding to help me. My greatest weakness moving into future math classes is my procrastination when it comes to math assignments, and I know that I will have to work on this skill moving forward in any of my future math endeavors.
The Polynomials & Art Project reflects our Algebra 2 class' knowledge of polynomials and graphing functions in the context of art and photographs. By learning more about the process of graphing and factoring functions through visualization, I was able to understand these concepts more easily, and I believe the rest of my class was as well. A large component of this project relied on using graphing calculators to determine local + global minimums and maximums, as well as determining accurate x-intercepts and scalars. By using this technology, our class was able to become more proficient using graphing calculators as well as doing these equations in writing as shown by the writing portion of this project.
When graphing polynomials, the “zeros” are a common term referring to the x-intercepts of the equation. The number of zeros can often be taken from the highest degree of a polynomial equation. For example, the equation F(x)=x3+2x2+4x would have 3 zeros since the highest degree is 3. To find a zero, there are two methods that one can use. The first method is factoring a polynomial into its simplest terms, and then using the zero product property to calculate the specified amount of zeros. The second method one can use it to factor the constant term into its positive and negative whole number factors. Once the factors have been identified, one can plug these negative and positive values in one by one to the original polynomial equation until the equation equals zero. Learning these two methods was very helpful in teaching me about algebraic equations as well as giving me a more in-depth understanding of quadratics.
During this project I learned that working with visual aspects really benefitted me as a learner. By taking a photograph and visualizing the lines I was going to graph, I was able to translate these lines onto paper much easier. This project made me feel comfortable with the the field of polynomials, and I am happy about how my final project came out. My biggest takeaway from this project was the skill of overcoming hard detail work and learning how to use scalars to find a “best fit” equation for a line. By learning these two skills, I’m sure that work in future math projects involving quadratics will be much easier. If I were to do this project over again, I would try to pick a picture that had 3 possible polynomial lines rather than two, so that I could get extra practice graphing and writing equations in this form.
If I were going to exhibit my project again, I would fix the title and my name on the board as well as add some interactive elements. My title and name could have used a little bit of refinement, and in hindsight I would have liked to print them out on a piece of paper and glue them on so that they would look more professional. As far as adding an interactive element, I would have liked to include my calculator and show people example functions on the screen so that they could understand the concept more completely. My greatest strength moving into future math classes is my will to learn and make mistakes. I know that there is still a lot that I have to learn in regards to math before I go to college, and I will use this understanding to help me. My greatest weakness moving into future math classes is my procrastination when it comes to math assignments, and I know that I will have to work on this skill moving forward in any of my future math endeavors.