[casualrandomcom]

They look symmetric to me, but that's not point anyway, I guess they are parables, only they are rotated, their axis is not parallel to the y axis.

If those are 2nd order functions in the 2d plane, then we don't agree on terminology.

The reason why I feel an expert is that it is clear at first sight to me that if you really implement the Newton method in that situation, the approximating functions that you will get are totally different from those that were drawn in the illustration.

The third parable from the left on the lower left figure, is definitely not a second order approximation to the target function: the convexity is reversed!

[MITSardine]

Well, now that you mention it, even the first one is on the wrong side of the graph. The second derivative is apparently (to my eyes) negative there, so the approximating parabola should be turning downwards. Whichever the sign, its value is close to zero anyways, the approximation would look very flat there.

Anyways, it's a little graph to illustrate the idea of a second order approximation, I think it does the job.

[ckemere]

The function is also not convex…