Basketball Quadratics

It's been awhile since I've had a math post on here, so I thought it might be time. At my school we are in the process of transitioning from our previous Algebra 1 course to an Algebra 1 course that aligns with the Common Core (Semester 1, Semester 2, although much of Semester 1 will go away next year as we complete the transition). As a result we are going much more in-depth on quadratics than we did previously.

To put this particular activity in context, we will have already discussed factoring, solving by factoring, graphing, completing the square, and quadratic formula. We then touch on graphing using the vertex form of a quadratic equation. As usual, I've borrowed ideas from wherever I can and, once again, this activity is from Dan Meyer.

I've previously done this activity using Geogebra, but with the recent addition of the ability to add images to Desmos, I decided to try to go that route. As is becoming a habit for me, I host the activity in a Google Doc and then link out from there.

One of my struggles is always how much direction to give the students, and I tend to fall on the side of probably giving too much scaffolding for them (compared to some other folks). My experience has been that if I don't, we don't get very far, but I still struggle with where that middle ground should be. So my compromise with myself is to give them a lot of scaffolding as we step through the first example, then turn them loose from there.

As always, I would love your constructive feedback on this.