As a student, I never understood why we set quadratics equations equal to zero and factored to solve them. This really irked me. An article a few years ago in Mathematics Teacher inspired this set of Math Labs. I have different groups of students work on each of these and present the results, then provide each student with a photocopy of the completed set. Each group also puts their graph on a poster-sized sheet of graph paper, and these stay up on my side wall throughout the year. We frequently come back to them, to remind them of the concepts such as double roots that these illustrate.
Labs 1 through 4 are parabolas, Lab 5 extends the lesson to show that the product of three linear functions is a cubic.