In one class I began by going over the homework from the textbook and in the other I went over their quiz. I think going over the homework was more helpful because question #5 led into what were going to do.
I put a equation on the board in factored form and then graphed it with Sketchpad. We discussed what we noticed about the graph and the equation, then confirmed it with other examples – that factored form gives us the x-intercepts (or roots). So I put a sketch of a parabola with two roots on the board and I labeled the roots, the y-intercept, and the vertex.
Using factored form and from what they did for homework, we changed the equation into standard form. I then had them look at the graph on the screen and got them to notice that the constant term was the y-intercept. I mentioned that was because if x = 0, then the x² and x terms would become zeros.
Then using what they learned in 9.2, we went from factored form to vertex form. Then, we transformed vertex form to general form. We also showed that it was the same as we got from our factored form. All the while, I had been putting each form in Sketchpad and graphing them so that the students could see that they were all the same graph. I reiterated that all three forms mean the same thing, but they just give us different information about the graph of the quadratic – the x-intercepts, the y-intercepts, and the vertex.
After that, I put another factored form on the board and had them find the general form as I walked around the room helping them. Then they had to find the vertex form. This was repeated once more – all kept on the board as well, before I gave them their homework, which were the CPM circle – factoring worksheets which I told them would help them go from standard form to factored form which we would do the following day.
