This is a combination of two different activities I created for my students to connect together, quadratic equations, factors, roots, and parabolas. I really wanted to help my students to deepen their understanding that these things work in concert together. It appeared to really help them and they seemed to enjoy working on these pages.
This activity is based upon the style of questions asked by the Smarter Balanced Assessment Consortium. Instead of simply asking students to pick the one correct answer from a group of 4 or 5 possible answers the students are engaged in a critical thinking activity where they will need to consider all givens as possibilities. Also by sorting the expressions the students are able to more clearly see patterns contained within factors of polynomials.
When I did this activity in my own classroom I had the students work in cooperative groups where they could discuss their findings with each other.