There are two types of problems in this "scavenger hunt":
8 problems - Students solve quadratic equations using the quadratic formula. Answers are expressed in exact form. (The answers do not require the skill of simplifying radicals, though, unless it's a perfect square.)
3 problems - Students use the discriminant to determine how many real solutions the quadratic equation has.
You post the 11 problems IN A RANDOM ORDER around the room. Either working independently or in a small group, students begin at any problem and solve it on lined paper. They then should find their answer typed on the top of another problem posted in the room, which brings them to that problem, and so on. If they do all 11 correctly, it should complete one loop, bringing them back to where they started.
My students had fun finding their answers and dashing from problem to problem. It was satisfying when they saw their answer posted, but if they didn't, they could try to revise on their own or check in with me for help. Teachers may wish to collect the students' lined paper at the end to ensure that everyone was working.
This activity is attached as a zipped file, containing a PDF of the 11 problems, an editable Word document of the 11 problems, and an answer key.
Note: If you prefer their answers to be written as rounded decimals, that would be easy to edit. If you want to swap out or add problems, you just have to make sure you maintain the scavenger hunt loop.