Polynomials & Art
Project Description
For this project, we started with a picture and had to find the curves (polynomials) of the picture, draw them, then create real equations with the points we found from our curves. After that we refined and adjusted our polynomials to assure that they fit with our equations. Then finally, we each created a new picture with the new adjusted polynomials. With my project, I started out with some cute kittens, found the polynomials surrounding their heads, and then turned it into an awesome whale.
Written Piece for the Project
A polynomial function is an expression of more than two algebraic terms, also known as a non-linear, or curved line, on a graph. The zeros of a polynomial function are the values where the function of X, f(x), equal zero. The simplified way to say it is where the polynomial crosses the x-axis (horizontal axis). Multiple zeros are when the polynomial is in factored form and the same zero shows up more than once. Imaginary zeros are theoretical in the sense that the polynomial never actually touches or crosses the x-axis, but the zero still exists. You can find a zero by observing at what points the line crosses the x axis, and those points are the zeros. Or you can find the zeros of a polynomial function if you have the equation for the polynomial and a Ti-84 calculator. Enter the equation on the y= page and hit graph. Then hit calc and select zero. It will ask you to select the left side of the curve, the right side, and then where you think the zero is. It will then give you the point of the zero.
A local minimum of a polynomial function is the lowest point in a curve of the polynomial. A local maximum of a polynomial function is the highest point on a single curve of the polynomial.
A local minimum of a polynomial function is the lowest point in a curve of the polynomial. A local maximum of a polynomial function is the highest point on a single curve of the polynomial.
Project Reflection
This was a cool project to do in math class because we had the freedom to have some fun and do some art. I also really liked being able to do a project in math because we normally have to stick to just normal boring math curriculum. I don't think I would change anything about this project because any more art or less math would take away from actually learning the content, but more math would not make this project more enjoyable, so it already has a great balance. The reason I chose to do my project the way I did is because I like cats, and then a friend gave me an idea for the whale and it ended up working perfectly with the polynomials I had.
Algebra II Semester 1
The piece of work that I am most proud of for first semester is my semester exam project. I did the challenge extension for this project so I had to create more hard problems and no easy ones. I am proud of this project because I expected it to be really tough but I got through it in the same time everybody else did. All of problems were high quality and actually made a lot of sense and all came to actual whole number answers, so they looked like they could have been in a textbook. The ridiculously hard problem I created was a word problem and in it I used real numbers for the speed of light and how far away other stars are away from us. Then when I typed up my problems I used a computer program called geogebra that we learned last year in geometry, to create the graph for my graphing inequalities problem, and it turned out great. I think I had some of the best problems in the class and all of my problems could be used in the semester exam.