Line of best fit for a Parabola?

If the points are experimental measureents (or are calculated from experimental measurements), do NOT force the curve to pass through the points.

Draw a smooth best-fit curve (no small wobbles) which passes nearby to the points. If you are lucky, it may even pass through some of the points.

A couple of examples in the links.

When eyeballing the curve fit, we ensure the number of data points above the curve all along the curve is the same number of data points below the curve. As to the shape of the curve, for that you need to rely on the physics in addition to the data point distributions. That results because there are typically several curve shapes that more or less fit the data. And when eyeballing, you are not precise enough to actually tell which curve (e.g., straight or parabola) is really the best one.

So if you're doing trajectories with your graphs, the parabola would be the best curve, so you place it so that the p(x,y) points above the line = the points below it. On the other hand, if you're doing A = F/M (Newt's Second), the straight line should be used to put as many data points above as below.

And, no, you don't draw in a "perfect" plot; you make the data points balance above and below. You are fitting the curve to those points.