By looking at the two cases, I have concluded that it is better to produce 5 graphs in a sequence by adding one at a time. I came to this conclusion by thinking about what would benefit the students directly. The first method (case 1) pops five graphs at once. This is done by either pre-made overheads or using a graphing calculator or software where all the graphs are the same color. It would be very easy for students to get confused of the equation of each parabola. This will not help in determining the effect of a, b, and c.

In case 2, the students can easily identify each parabola with each equation. Another benefit is that student questions can be answered immediately. If a student wants a to be a negative value or a fraction, all you have to do is graph it to answer the question. Case 2 develops an environment that is more student friendly and should encourage more exploration.

 case 1

case 2

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