# 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."  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.