Linear to Quadratic Equations

This is an idea I picked up from an article in Mathematics Teacher.

After students get used to linear equations you have to ask what interesting things can we do with linear equations besides draw lines? What if we add two linear equations? Well, obviously you just get another line. Not too interesting. But what if we multiply two linear equations together?

Make a chart
x|y₁|y₂|y₁×y₂

(x,y₁) plots the first linear equation
(x,y₂) plots the second linear equation
(x,y₁×y₂) plots a new function

Now you can introduce the quadratic equation and look at how the y-intercept is the product of the b's in the linear equations and the x-intercepts are the opposite sign of each b in the linear equations.

After you've done all your quadratic work, try dividing a linear equation by another linear equation or try multiplying three linear equations. Both are interesting and essential topics in Algebra.

Geometer's Sketchpad makes a perfect platform for investigating these equations.