How to know the form of a line in a graph without any calculation? [closed]

My Physics book has many graphs. Some are straight lines, some parabolas while others are hyperbolas. I have not studied these curves (conic sections) yet and to me parabola and hyperbola look just the same. Is there any way of knowing whether a line is a parabola or a hyperbola just by seeing the graph of the line.

closed as unclear what you're asking by Math1000, Vladhagen, Shailesh, BruceET, hardmathJan 14 '17 at 1:48

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• Hyperbolas have asymptotes whereas parabolas aren't usually bounded in the $x$ direction (or $y$ direction if you consider those parabolas) If you want to do a little calculation, then choose three points on the graph. Since there's a unique parabola that fits those three points, find it, draw it and if it matches, it was a parabola. Otherwise, it was some other function (possibly a hyperbola). – user12345 Jan 13 '17 at 17:39
• It really depends how carefully and completely the graph is drawn. If you zoom in close enough on the vertex of a parabola, it's practically indistinguishable even from a circle, although if you zoom out far enough the difference will become obvious. – David K Jan 13 '17 at 17:40
• It would seem preferable to refer to lines as special kinds of curves, rather than to refer (as the title seems to) to curves as "lines". – hardmath Jan 14 '17 at 1:47