Scientific fertilization is an important technical means of achieving high and stable peanut yields. Using soil testing and formula fertilization, the “3414” optimal regression design was used and included 14 nitrogen (N), phosphorus (P), and potassium (K) fertilization treatments. Ternary quadratic functions of the fertilizer effect were established according to three-season field experiments and the regression analysis of fertilizer–yield function was performed to explore the optimal fertilizer application mode and ratio for peanuts under mulched drip irrigation (MDI), and a suitable fertilizer application system was established. The ternary quadratic equation relating peanut yield (y) and the fertilizer application rates of N (N), P (P2O5), and K (K2O) was obtained after fitting, i.e., y = 2912.528 + 21.432N + 16.324P + 6.181K − 0.051N2 − 0.109P2 − 0.061K2 + 0.017NP + 0.023NK + 0.086PK, and significance analysis and typicality assessment were performed. The model R
2 was 0.9709, both values are extremely significant (p < 0.01), which indicates that the obtained ternary quadratic fertilizer effect function is typical and could be used for statistical purposes and fertilization recommendations. Three quadratic fertilizer effect functions were obtained. Among them, the equation for K is extremely significant, and the equations of N and P are significant. According to the assumption that the marginal yield is zero and the marginal profit is zero, the fertilizer application rate with the maximum yield, the fertilizer application rate with the best economic benefits, and the corresponding yields were obtained. The optimal fertilizer application rate predicted by the ternary quadratic fertilizer effect function was relatively high, so the three quadratic fertilizer effect functions were used for prediction. Under the test conditions, the recommended fertilizer application rates for peanuts under MDI are 256.6 kg N per ha, 164.2 kg P2O5 per ha, and 213.2 kg K2O per ha, the recommended fertilization ratio is 1:0.64:0.83, and the recommended ratio under formula fertilization is 23:15:19. The study has developed a data-based decision support system for Xinjiang drip-irrigated peanut, which assists farmers and agricultural managers in making more scientific and precise fertilization decisions based on the specific growth requirements of the crops and soil conditions. This evidence-based methodology enhances the precision of agricultural management, which is conducive to increasing crop yields while reducing resource wastage and environmental impact. However, multipoint and multiyear experiments are still needed to ensure that the findings are adaptable to the diverse soil conditions and fluctuating climate patterns that may be encountered in practice.
