A teaching activity that makes the equivalence and zeros connection between functions. Parts 1 through 3. Use with Foundations for College Mathematics, Ch. 3.4, 3.5.
Before the Activity
Download the attached StudyCards™ file to students' calculators.
During the Activity
Part I - makes the equivalence and zeros connection between, for example, the function y = (x - 3)(x + 2) and y = x2 - x - 6. All quadratics included have a leading coefficient of 1.
Part II - makes the equivalence and zeros connection between, for example, the function y = (2x - 3)(5x + 2) and y = 10x2 - 11x - 6. All quadratics included have a leading coefficient of something other than 1.
Part III - makes the argument that if you know the zeros of, for example, y = (2x - 1)(x + 3), (whether through the parameter-zero connection or using a graphing calculator), and you know the equivalence to y = 2x2 + 5x - 3, then if you start with a function like y = 2x2 + 5x - 3 and find the zeros using a graphing calculator, you know it is equivalent to y = (2x - 1)(x + 3). Thus, students can now factor with the graph of the function.
After the Activity
Review student answers
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary