I haven't worked with gas analyzers, but for most chromatography applications it is usually recommended to not force the origin with linear or quadratic calibration curves. Also it is not recommended to calibrate using quadratic fit with anything less than 5 points. With only three points how can you know if the curvature of the quadratic fit is actually a curved response fit or simply curvature induced by one point being slightly inaccurate?
Actually most of the calibrations I do have 7+ points so you can easily tell if it is going to be linear or quadratic.
As for a TCD being linear, it will depend on how many orders of magnitude you are calibrating across. For the best accuracy you should have calibration points that are at the upper and lower concentrations you will report, with ones in the middle to fill in the shape of the curve. For EPA regulated work like I do, reporting results above or below your highest and lowest calibration points is considered invalid.
I used to do metals analysis where the ICAP was considered "linear over five orders of magnitude" which does hold up when you are in the upper ranges, but once you are working near the Limit of Detection in trace analysis that falls apart quickly. The method said to calibrate with a 1ppm standard and a blank with the limit of detection at 5ppm. Problem was when you ran a standard at 10ppb sometimes it would calculate out to be 40ppb or -20ppb, which is fine if you are worried about values in the ppm range but not if you need to know values near 10ppb required reporting levels. So whatever detector you are using, be sure to check it at the limits of what you expect samples to be and at the lowest level you wish to report as a positive result.