Linear, quadratic and cubic moduli

|u|=u when u 0, and |u|=-u when u<0. To draw y=|f(x)|, keep every part on or above the horizontal axis and reflect only the parts below it. Zeros stay in place; negative turning values become positive. The domain is unchanged. For y=|x-1|, the vertex is (1,0), with slopes -1 and 1. For y=|x2-4|, reflect the portion between -2 and 2; (0,-4) becomes (0,4). For y=|(x+2)(x-1)(x-3)|, mark roots -2,1,3 and the vertical intercept 6. The original cubic changes sign at each simple root. A double root touches the axis; a triple root still crosses it. More generally, even multiplicity touches and odd multiplicity crosses.