The module function approximation by Bernstein polynomials

We obtain all the basic formulas connected with the approximation of $f(x)=|2x-1|$ by Bernstein polynomials. The estimates of the maximal coefficients in the polynomials are given. Degree of approximation for different points $x\in[0,1]$ is investigated. It is shown that near the point $x=1/2$ acceptable degree of approximation achieved on polynomials which are not computable from a practical point of view.