The Gaia-Sausage-Enceladus merger was a major event in the history of the Milky Way. Debris from this merger has been extensively studied with full kinematic data from the Gaia mission. Understanding the star formation history of the progenitor galaxy aids in our understanding of the evolution of the Milky Way and galaxy formation in general. We aimed to constrain the star formation history of the Gaia-Sausage-Enceladus progenitor galaxy using elemental abundances of member stars. Previous studies on Milky Way satellite dwarf galaxies show that key elemental abundance patterns, which probe different nucleosynthetic channels, reflect the host galaxy's star formation history. We gathered Mg, Fe, Ba, and Eu abundance measurements for Gaia-Sausage-Enceladus stars from the SAGA database. Gaia-Sausage-Enceladus members were selected kinematically. Inspired by previous studies, we used Fe/Mg Ba/Mg Eu/Mg and Eu/Ba as a function of Fe/H to constrain the star formation history of Gaia-Sausage-Enceladus. We used the known star formation histories and elemental abundance patterns of the Sculptor and Fornax dwarf spheroidal galaxies as a comparison. The elemental abundance ratios of Fe/Mg Ba/Mg Eu/Mg and Eu/Ba all increase with Fe/H in Gaia-Sausage-Enceladus. The Eu/Mg begins to increase at Fe/H -2.0$ and continues steadily, contrasting with the trend observed in the Sculptor dSph galaxy. The Eu/Ba increases and remains high across the Fe/H range, unlike the pattern seen in the Sculptor dSph galaxy, and deviates from the Fornax dSph galaxy at high Fe/H . The Ba/Mg is higher than those of the Sculptor dSph galaxy at the lowest Fe/H and gradually increases, similar to the Fornax dSph galaxy. We constrained three main properties of the Gaia-Sausage-Enceladus star formation history: 1) star formation started gradually, 2) it extended for over 2 Gyr, and 3) it was quenched around Fe/H of $-0.5$, likely when it fell into the Milky Way. We show that the elemental abundance ratios Fe/Mg Ba/Mg Eu/Mg and Eu/Ba can be used to trace the star formation history of a disrupted galaxy when these measurements are available over an Fe/H range that is representative of the progenitor galaxy's stellar population.