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It sounds as if you have your lesson! I am not sure what you need. Give the students a list of the equations, or the general form and list of the coefficients, and ask them to graph over a specified interval. Perhaps you want to organize the information into a chart where the students fill in the chart. The TI-82 has a feature that will give the exact roots no matter what window the students are in. (Have them press 2nd and then CALC above TRACE.) This will give the roots. The TI-82 will also find the maximum or the minimum value (also found on the same CALC menu). You could have them explore the relationship between the vertex and the coefficients. You could have them note the relation of the roots to the equation. You could use the discriminant and have them realize what it means if D is +, -, or zero. I hope this is what you needed. Do you need more instructions with the TI? Let us know.
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