Polynomials and Art Project

For this project we out lined an image using polynomials then recreated a new image from the polynomials drawn. To make these polynomials we placed a clear piece of graph paper of the image then drew the x and y axis. Each part of the polynomial that crosses the x-axis is called a zero.  In most cases when you think of zero, it is not actually zero, only y=o, however x can be any number. 

Written Piece

Zeroes are the x-coordinates of the points where its graph meets the x-axis. However zeros don’t have to cross the x-axis but can be a curve below or above the x-axis. In that case the zero would be imaginary. If there are two zeros then the polynomial passes through the x-intercept two times, and if there are three zeros then it passes through the x-intercept three times, and so on. When you think of zero, it is not actually zero, only y=o, however x can be any number. The farther apart the zeros the wider the curves will be in the polynomial. Another name for the zeros in a function is called the x-intercepts. One way to find a zero is make y equal zero. From there you would factor the expression and solve for x for each factor.

 The local minimum and maximum point in a polynomial function are the lowest points on the polynomial and the highest points. To clarify, the value of the function where at its maximum point is called the maximum value, and the point where the function is at its smallest point is called the minimum value. They show how far the curve of the polynomial goes from the x-axis. It is crucial when graphing polynomials to know the minimum and maximum values. But when graphing a certain part of a polynomial you may not be able to see all the minimum and maximum points, in this case you would be graphing the local minimum and maximum points, which are the highest and lowest points that can be seen in the window of what is being graphed. 

Project Reflection

This project was not as effective as I hoped because the problem I had with doing this project was that we did this about three months ago, so now it is hard to remember all of the concepts we learned. However we had a written part of this project were we had to explain what we did. And after reading this it all came back to me, and I was grateful we came back to exhibit this project because now I feel I learned it better.

Relating this project to real life depends on the profession you want to get into this project can be related to real life. If you want to become an architect knowing polynomials would be good to know, and building bridges require polynomials.

The hardest part about this project was keeping the project simple. It was really easy to get too complicated and when you got to the calculations part you find your self befuddled not knowing what to do. So it was hard for me just to keep it simple. 

Semester Reflection 

For the Linear Equations Mini-Project we had to create a landscape picture using linear equations and inequalities. I chose this assignment as one that I am especially proud of because I decided to go above and beyond and do the challenge extension. With the challenge extension the only lines and shading (coloring) that could be done were one that can be represented by an equation or inequality. I feel especially proud of this assignment because I gave the extra effort to go above and beyond. This was also very challenging because lines that stopped on our paper than it must be represented by a line segment with a domain and range for that segment. I never really mastered graphing segments so I had to go and make time during Cross Country to talk over with Effi about how to graph segments.

Not from this project alone but all the projects, assignments, and tests this semester in Algebra 2 I have learned to be an active learner and a collaborator. Being an active learner means when you don’t understand something you take the initiative to make sure you understand it. I have done this by using Khanacademy.org and advocating to Effi if I don’t understand something. But succeeding this semester also means using your peers and learning to work together to understand content. Nick, or as many know him as Magic Nick, has been one person this semester that has really helped me understand all the things need to know and helped me succeed as a math student. Because of being an active student and a collaborator I have learned to succeed in math this semester.