Semester Exam Project:
For this project we had to create our own semester exam. I am proudest of this piece of work because as I was doing it I realized how much I have learned in this class over the semester. I am also proud because I think i did really well on creating problems that exhibit what they were supposed to one or two of them even made it on the final exam. From this project I learned that I know and retained more than I actually thought I did. This project was a really good review for me, being able to go back and revisit what I learned over the course of the semester.
Semester Math Project | |
File Size: | 55 kb |
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Polynomials and Art Project
For this project we choose a picture that had both curves and lines in it so that we could create either polynomials or parabolas from our picture. I choose an umbrella as my picture and created both a polynomial and a parabola from my picture. We then had to write equations and find the zeros for each of our lines and curves. After we wrote them we had to recreate our lines and curves from the equations on a transparency sheet. From this recreated polynomials and parabolas we made our own art piece. I created a turtle from my umbrella.
Written Piece:
When you are finding a zero of a function, you are looking for input values that cause your functional value to be equal to zero. To find a zero, first you need to make a factor of f(x) equal to zero, then by using synthetic division you can find the other factors. This is a method used to divide a polynomial by the divisor of the form x-k. For an example, see the picture below. Once you get your answer, you can plug them back into factor form, which will give you your x-intercepts. Because of some exceptions, not all zeros are x-intercepts. An exceptions is imaginary zeros, which are the x-values, when the graph curves, that are above or below the x-axis. Another exception is a multiple zero, which is when the same zero is repeated more than once in a polynomial. A local maximum of the function is the point that is higher than all near by points and the local minimum of the function is the point that is lower than all nearby points. The global maximum of the function is the absolute highest on a polynomial graph and the global minimum of the function is the absolute lowest on a polynomial graph.
Synthetic Division Example:
Synthetic Division Example:
Reflection:
I really enjoyed making my own art piece from a completely different art piece using just math: equations, polynomials, and parabolas. In this project I learned how to write equations from a given line and how to find the zero/zeros of a line (as you see above). If I were to do this project again, I would find a harder picture to find lines in to challenge myself, I would also have done the challenge extension of this project to challenge me as well. One other thing I would have done differently would have been to refine my writing and equations. But over all I think this project went really well and I enjoyed do it.