How can I describe quadratic problems associate with each level of Bloom's Taxonomy?
I am assuming you mean Bloom's Revisied Taxonomy, since that seems to be more in use. I’ll give it a shot:
The lowest level, REMEMBERING, would include labeling an equation as a quadratic (as opposed to linear), identifying quadratics from a list of equations, and possibly describing characteristics of a quadratic.
UNDERSTANDING would take an equation and ask a student to tell whether it is a quadratic and then explain why or why not and then maybe tell what could make it a quadratic (saying, “If you made the x into an x^2…”).
APPLYING would have students manipulating and solving quadratics. I would say finding zeroes by factoring falls into this area.
Completing the square is a quadratic application that requires ANALYZING. Students have to examine the equation, decide what is needed to make the quadratic work, reorganize and reconstruct the equation to make it into the quadratic they need.
Examining a variety of methods of solving quadratics would be a good way to get students EVALUATING. Take a random quadratic and have everyone solve using their own choice of method. Share solutions and have a discussion. Which method was most efficient? Which was easiest? Why might you prefer to use this method or that one? You can also present problems that are incorrectly solved and have students try to figure out the error and correct it with words (not just doing it algebraically).
Finding real-world examples of problems that could be solved using quadratics is one way to get students CREATING. Students would write the problems themselves and then, of course, solve them. Also, if students can find other ways to solve quadratics that are not algorithms taught, this is the highest level.