= Quadratic spline
{title2=$q\in C^1,\quad q|_{(x_i,x_{i+1})}\in\mathcal P_2$}
A quadratic <spline> with simple knots is a continuously differentiable <function> that is a <polynomial> of degree at most two between successive knots. Its first <derivative> is continuous and piecewise linear, while its second <derivative> is piecewise constant and can jump at knots. Constant tails impose vanishing first derivatives at the outermost knots. Such a spline arises from first-derivative roughness penalization when observations are interval averages, as in the <quadratic smoothing spline for interval averages>.
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