Let d(c) denote the Hausdorff dimension of the Julia set of the polynomial z²+c. First we will consider the "first" parabolic parameter: 1/4 (one petal). We will prove that d'(c) tends to infinity, when c tends to 1/4 from the left (the result of G. Havard and M. Zinsmeister). Next, we will discuss behaviour of d'(c) close to other real parabolic parameters.