## Thursday, January 25, 2007

### Next Lesson: Creating a cubic function from 3 linear functions

Intersession is nearing completion, and I am finally getting back on track with my curriculum. My Algebra 2 students had their Quadratics and Complex functions test today, which I hope to grade later tonight, but we'll see...

Tomorrow, we have a short class, and it works out well, because we're going to do a little exploration type activity. On the homework that is due tomorrow, I gave them a graph with two linear functions on it; there are guiding questions that help them graph the sum of the functions both graphically and algebraically, and then to compare their results. Then, the second part asks them to repeat the process, but finding the product instead of the sum. This is a neat way of visually understanding why the product of two linear factors yields a parabola, and why the zeroes of the parabola are at the zeroes of the lines. So tomorrow, students will repeat this activity, this time graphing the product of three lines to generate a cubic function. We will focus on the roots of this product function, and how the roots split the x-axis into intervals, and how you can easily determine the sign of the product function within any given interval.

I hope that this will lay a good foundation for later on when we use number lines to sketch polynomial functions and solve inequalities in factored form.

I am posting the worksheets for this on ILoveMath. If you use it, let me know what you think.

#### 1 comment:

mrc said...

This is a really cool idea. As you know, I am all about number lines. But the idea of showing the zero product property, graphically, and showing how the signs of the various linear terms contribute to the sign of the product, that is REALLY COOL. This makes the concept of roots so much more concrete and graspable.