1σ (dark colours) and 4σ (light colours) error contours in the (a₂,  a₃,  a₄) parameter space resulting from fitting the data using Eq. (8) for the samples Pantheon+quasars and Pantheon+quasars+GRBs. We plot the 1σ and 2σ error contours for the Pantheon+GRBs. The black solid line represents a flat ΛCDM model with Ω_M in the interval 0.1–0.9, where the black point marks the value Ω_M = 0.3 (i.e. Eqs. (9)–(11)). From top to bottom: result from the cosmographic technique described in Sects. 3.2 and 4.2.