Is it possible to have a quadratic spline and a cubic spline meeting and being C2 continuous at a point K?

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I'm trying to interpolate some datapoints. Ideally I would like to have 3 splines: The first and third being quadratic, and the second one (in the middle) cubic. Is it possible to mix polynomials and still have C2 continuity at every point in this context? Or should I just use 3 cubic splines directly?