The \(\alpha \) -energy of a graph G with n vertices and m edges is defined by \(E^{A_\alpha }(G)=\sum _{i=1}^n\left| \lambda _i^\alpha -\frac{2 \alpha m}{n}\right| \) , where \(\lambda _i^\alpha \) denotes the i-th largest eigenvalue of the \(A_\alpha \) -matrix of G. In this paper, we first establish a sharp lower bound for the \(A_\alpha \) -spectral radius of a graph in terms of its degree and average 2-degree, thereby refining and extending the classical bound \(\lambda _1^\alpha (G)\ge \tfrac{1}{2}\Big (\alpha (\Delta +1)+\sqrt{\alpha ^2(\Delta +1)^2+4\Delta (1-2\alpha )}\Big )\) . As applications, we derive tight lower and upper bounds on the \(\alpha \) -energy of connected graphs and provide a complete characterization of all extremal graphs attaining these bounds. Our results unify and generalize several existing conclusions, including the signless Laplacian energy bounds of Chen et al. (2026) and the \(\alpha \) -energy bounds of Pirzada et al. (2021).
