Here's a very simple web-based graphing machine to help students get an intuitive "feel" for how its graph changes as the parameters vary. It works for a wide range of equations and includes slider bars for each parameter, and animation so students get an intuitive feel for how any given parameter affects the graph. This is a great tool for Algebra 1, Geometry, and Algebra 2 students - hence the name: GeoGebra. For an example of how it works, check out the YouTube video embedded in this web page (below). 

If the video looks interesting, you can access the program on the web at GeoGebra. Once there you can begin experimenting with equations of all sorts, and if you sign up for a free account then you can even save your work. Start by typing a simple equation, like y=mx+b, into the box near the upper left, then hit Enter. When it asks you if you want sliders, say yes. If you need to, you can clear the input box by going to the top right of the screen and click on the 3-horizontal bar menu item, then click on New. Experiment with the simple straight line for a few minutes. Then put in a quadratic and do the same thing. When you get to the point of needing to insert a number squared, use the onscreen keyboard (instead of using x^2).

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