Is it appropriate to describe the function $$f(x) = \binom{x}{2}$$ as parabolic? How does it vary over $c$: $$f(x) = \binom{x}{c}?$$ And, is there any intuition behind these graphs? For example, their resemblance to the polynomials of degree $c?$
I tried inputting one into wolfram alpha and it spat out a continuous function, which confused me. This is what prompted me to ask the question.