I suspect it's a [modified] section of a parabola, so short that it's hard to differentiate it from a straight line.

A flying spark is a piece of incandescent metal or other matter ejected from some glowing object; we see its trajectory because it's hot enough to give off light. When/if at some point it bursts into pieces, still glowing, each piece is thrown out into its own path. After they cool off we don't see them, but [except for air resistance] they're all still just falling bodies with an initial velocity, and the paths are all parabolic. "S = 1/2 a t squared" or some variation of that.

[Of course air resistance can be considerable for objects that small, so the deviation from a true parabola may be quite significant.]


Edit: On rereading, I suspect you weren't asking for the name of the shape of the line at all...but I think the gist of what I said covers what you were getting at, so maybe I did answer the question after all.