# Multiplicity of Zeros and Graphs Polynomials

An app is used to explore the effects of multiplicities of zeros and the leading coefficient on the graphs of polynomials the form: \[ f(x) = a(x-z_1)(x-z_2)(x-z_3)(x-z_4)(x-z_5) \]

With this factored form, you can change the values of the leading coefficient a and the 5 zeros \( z_1, z_2, z_3, z_4 \) and \( z_5 \). You can explore the local behavior of the graphs of these polynomials near zeros with multiplicity greater than 1.
## Interactive Tutorial on Zeros of PolynomialsClick the button "Plot Polynomial" to start.You may hover the mousse cursor over the graph to trace the coordinates. You may also Hover the mousse cursor on the top right of the graph to have the option to download the graph as a png file. Some activities that you may wish to go through are listed below. |