Lab07 Polynomial Graphs and Complex Numbers

1) Zeros of a Polynomial

Use the equation of the polynomial function and the graph provided in the applet below. 

2) Alternative Methods of Finding Polynomial Zeros

Watch Mr. McLogan find the zeros of the cubic polynomial using synthetic division. An alternative method is to multiply the factors  to get a quadratic expression and then use long division to extract both roots at the same time. 

3) Graphs of Complex Numbers

Watch Theschoolofchuck's video below until time 4:00 with the volume muted. 

4) The Mandelbrot Set

"More precisely, the Mandelbrot set is the set of values of c in thecomplex plane for which the orbit of 0 under iteration of the complex quadratic polynomial remains bounded.[1]"  Read more on Wikipedia! This graph uses a recursive formula   to generate the points of the graph. It says, to find a point, square the previous point and add on the complex number, c. Explore the applet by moving point c (now at the origin). As discussed in the video above, this is not on an (x, y) real number coordinate plane but instead on a (real, complex) coordinate plane.