I am categorizing types of math problems on the ACT. I started off with 'quadratic function' as one category, and 'conic sections' as another... It seemed like a simple classification at first, but then, I started thinking about it.....
What WOULD be the difference between a quadratic function and a conic section? Since a quadratic function is a parabola, and a parabola is a conic section...? Would it be like 'all poodles are dogs, but not all dogs are poodles'... or is does it depend on the context?
We can imagine that all the conic sections can be divided into:-
(1) Pair of straight lines; (2) Ellipses; (3) Hyperbolas and (4) Parabolas.
However, the set of Parabolas can further be subdivided into another subset whose axes of symmetries are only vertical. Quadratic function belongs to this category.
Added:-