algebra II
POLYNOMIALS IN ART
In this project we learned all about polynomials and how they work. We first had to choose a picture in art with a lot of curves. We then had to draw an x axis and a y axis on the picture and find a line that best fit it. We then had to work with the equations of those lines, and then we had to draw a new picture fitting in those lines.
A zero is a point where a line passes through the x axis, there are also imaginary zeros, which happens when you get a number from factoring an equation that is not actually a real number. You can find the zeros of a parabola by looking at a graph and finding where the line passes through the x-axis. The x axis is the horizontal axis. You can also find an x intercept by using the zero product property, which lets us find out what x is when our y is equal to 0. Make y equal to 0 in one of our equations, and figure out what x equals by solving the equation. You could also make a table to find what x equals when y equals 0. There may also be multiple zeros, which means that you get the same zero multiple times. The global maximum of a polynomial is the highest point on a curve in a polynomial, and the global minimum is the lowest point on a curve in a polynomial. The local maximum of a parabola is the point at which one curve reaches it’s highest point. The local minimum of a parabolas the point at which one curve reaches its lowest point.
Zeros
Polynomial: (0,0), (-7,0), (6,0)
Parabola: (-7,0), (1,0)
Factored form Equations
Polynomial: y=-.047(x-0)(x+7)(x-6)
Parabola: y= -.56(x+7)(x-1)
Polynomial
-Maximum point: (3.4, 4.3)
-Minimum point: (-4.1, -5.6)
Parabola
-Maximum point:(-3, 8.96)
Parabola
y= -.047(x-0)(x+7)(x-6)
y= -.047(x2 +7x)(x-6)
y= -.047(x3 + x -42x)
Expanded Form:
y=-.047x3 -.047x2 +1.97x
Polynomial
y= -.56(x+7)(x-1)
y= -.56(x2+6x-7)
Expanded Form
y=-.56x2-3.36x+3.92
Zeros
Polynomial: (0,0), (-7,0), (6,0)
Parabola: (-7,0), (1,0)
Factored form Equations
Polynomial: y=-.047(x-0)(x+7)(x-6)
Parabola: y= -.56(x+7)(x-1)
Polynomial
-Maximum point: (3.4, 4.3)
-Minimum point: (-4.1, -5.6)
Parabola
-Maximum point:(-3, 8.96)
Parabola
y= -.047(x-0)(x+7)(x-6)
y= -.047(x2 +7x)(x-6)
y= -.047(x3 + x -42x)
Expanded Form:
y=-.047x3 -.047x2 +1.97x
Polynomial
y= -.56(x+7)(x-1)
y= -.56(x2+6x-7)
Expanded Form
y=-.56x2-3.36x+3.92
Reflection:
This project was really challenging. Finding a line that fit the picture was a very difficult process, as well as the math involved with the lines. Most of it was a bit too easy for me though. If I were to redo this project, I would re-draw the second image to look better, because it was sloppy.
This project was really challenging. Finding a line that fit the picture was a very difficult process, as well as the math involved with the lines. Most of it was a bit too easy for me though. If I were to redo this project, I would re-draw the second image to look better, because it was sloppy.