Art & Polynomials
For this project we used our knowledge learned in class about polynomials, to recreate a picture with polynomials.
When you talk about a zero as used in polynomials it is simply referring to the x-intercepts of the polynomial. There are many methods to find a zero, most of which I will discuss shortly. One way is through multiple zeros. Multiple zeros are zeros that occur more than once in an a given occasion. An imaginary zero is when you have an imaginary number in your equation and you are trying to write it out. One way to find zeros is by using the rational zero theorem. This involves factoring the constant term by the leading coefficient. The constant term being the last number in the equation which is then split into many different factors of the constant, example: 12 – 1, 2, 3, 4, 5, 6 and 12. The leading coefficient is the number that is being multiplied by the variable with the highest degree, example: 1. Another way to find a zero is by the factor theorem. A polynomial f(x) has a factor x-k if and only if f(k) = 0. This process is called synthetic division. For example:
f(x) =1x3 -2x2-2x-3 x-3 is the factor of f(x).
The next thing you need to find when figuring out the zero for your polynomial is your minimum and maximum numbers. To find your minimum and maximum number you want to use your calculator to draw out the polynomial with the preexisting points. Then you are going to plot points using two opposing points on each side of the toughs and peaks. This process determines what the bottom of the troughs and the tops of the peaks depth or height is. This height is the maximum and minimum numbers are.
For this project I chose an image that I took back-country skiing that had a lot of different curves lines. I then drew lines on the curves and created polynomials from the image using those lines to create a new image. I thought this project was fun because I enjoy drawing and we were allowed to draw.
When you talk about a zero as used in polynomials it is simply referring to the x-intercepts of the polynomial. There are many methods to find a zero, most of which I will discuss shortly. One way is through multiple zeros. Multiple zeros are zeros that occur more than once in an a given occasion. An imaginary zero is when you have an imaginary number in your equation and you are trying to write it out. One way to find zeros is by using the rational zero theorem. This involves factoring the constant term by the leading coefficient. The constant term being the last number in the equation which is then split into many different factors of the constant, example: 12 – 1, 2, 3, 4, 5, 6 and 12. The leading coefficient is the number that is being multiplied by the variable with the highest degree, example: 1. Another way to find a zero is by the factor theorem. A polynomial f(x) has a factor x-k if and only if f(k) = 0. This process is called synthetic division. For example:
f(x) =1x3 -2x2-2x-3 x-3 is the factor of f(x).
The next thing you need to find when figuring out the zero for your polynomial is your minimum and maximum numbers. To find your minimum and maximum number you want to use your calculator to draw out the polynomial with the preexisting points. Then you are going to plot points using two opposing points on each side of the toughs and peaks. This process determines what the bottom of the troughs and the tops of the peaks depth or height is. This height is the maximum and minimum numbers are.
For this project I chose an image that I took back-country skiing that had a lot of different curves lines. I then drew lines on the curves and created polynomials from the image using those lines to create a new image. I thought this project was fun because I enjoy drawing and we were allowed to draw.