Getting to the bottom of things

Multiplying two Binomials  You've used the FOIL method for multiplying binomial expressions, but if you're like most of us, you just plugged and chugged to get the work done. Here's a tool that allows you to play with the values and see how changing individual parameters changes the graph of the equation. Tick the box for perfect squares and see what varying a parameter on a square does to the plot!
Multiply two Binomials; Plot the Quadratic

Multiplying three Binomials  That tool is for multiplying two binomial expressions, but what about three? Here's a tool that allows you to change the parameters in isolation on any part of three binomials and immediately see the change. This tool shows you a plot of the cubic instantly, and includes a checkbox to constrain the equations to perfect cubes.
Multiply three Binomials; Plot the Cubic

Charting Polynomial Expressions  Gain an intuitive sense of how each term in a polynomial influences the graph of the combined function. This tool displays the plot of your equation (up to degree 6) instantly, as you put it in, and updates the graph as soon as you modify it. Tick the box to enable the display of the first derivative of your equation (both the equation of the first derivative and its plot are displayed and updated on any change to the original function). The plot of the equation shows the value of the equation for each point along the x-axis; the first derivative plot shows how steep the original function is at each point.
Polynomial Equation Plotter

Charting Parametric Expressions  Parametric equations are a more general form of the regular plots taught in school. Rather than using the x-axis as the independent axis, these use an undisplayed independent axis called t. Both x and y are dependent axes, and x and y are shown in relation to each other at each point along t. To get a plot out of a parametric plotter, enter an expression (up to a 6th degree polynomial) for x and an expression (up to a 6th degree polynomial) for y. Or, lock one of the dependent axes to be the first derivative of the other dependent axis!
Parametric Polynomial Equation Plotter

Lissajous  Lissajous patterns show one sine wave in relation to another sine wave. One is plotted vertically and one is plotted horizontally, and interesting patterns are displayed. Note that one axis is plotted sine and the other is cosine, so equal frequencies plot as a circle.
Lissajous Plotter   

Doppler Shift interactive Demonstration  This demonstration permits you to learn interactivly about the "Doppler Shift." In this, you move the "transmitter" manually, and the transmissions are "heard" by a stationary microphone. Slowly move the mouse closer to the microphone, and see how the transmitted waves bunch up. It's often easier to hear a difference than to see a difference, so you have a choice: make the page produce sounds by clicking on the screen. If you don't click the screen, the page remains silent.
NOTE: the demonstration does work best with Microsoft Edge.
The Doppler Shift demonstration

Use this interactive tool to show the parameters of a real or hypothesized subnet. Suppose you know the IP address of one device on a subnet, and you know the Subnet Mask. From those two pieces of information, the subnet's Network ID, size of the subnet, and subnet broadcast address can be determined. This tool does the work for you. Input an IP address and a subnet mask, and all those are provided.
Subnetting (IPv4)