The atomic nuclei in the Zirconium isotopic chain show a ground-state shape transition uniquely pronounced in the nuclear chart with respect to its abruptness. Between the (mostly) ground-state spherical 96Zr and the ground-state deformed 100Zr, 98Zr lies somewhere between the beginning and the ending of this narrow transition area. This work quantifies the sudden onset of quadrupole collectivity at the transitional nucleus 98Zr. As measure for quadrupole collectivity, the first-time determination of the B(E2;2+ -> 0+g.s.) transition strength value of 98Zr was performed: A Coulomb excitation experiment with a radioactive 98Zr ion beam at the Argonne National Laboratory (USA) yielded a decisively small upper limit for the transition strength of interest. Complementary, the respective lifetime of the 2+1 level was measured with the RDDS method employing a 96Zr(18O, 16O)98Zr two-neutron transfer reaction at IFIN-HH (Romania). The analysis of the two independent experiments is described and the results combined and discussed. The findings are compared to recent theory and confirm the predicted shape coexistence in 98Zr as effect of type-II shell evolution. Consequently, the nucleus 98Zr is placed at the brink of the examined structural change and identified as closest nucleus to the critical point of the underlying quantum phase transition.