I found this activity a long time ago so I apologize, I don't know where to give credit. If you know, let me know and I will add it. I have always done it in Algebra 2 but with the new common core, we have brought it into our Algebra I classes for freshmen. My colleague wasn't sure they would be able to handle it, but they rose to the occasion. It is a great packet. The students work in groups of 4 and go through it page by page with their calculator to hopefully see some patterns emerge as they compare similarities and differences along the way. Eventually, they are asked to try one without the calculator and this is where it gets hairy and they start to see that they don't really get it yet. I let them struggle, talk to each other, finish it at home, just to make some sense of it. It is good for them. Then, the next class, we will share out and see what they come up with. I will answer questions and try to make the connections if they aren't seeing them. New this year, I came up with a practice worksheet for the second day. I must say, I think it is beautiful. Thanks @desmos!
Graphing Polynomial Investigation Lab
Here is the follow up: Poly Graphing Practice It looks a little funny in drop box. It is supposed to be two pages, each with a 2x3 table on it.
Have fun graphing!