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Living organisms are required to sense the environment accurately in order to ensure appropriate responses. The accuracy of estimating the environmental input is severely limited by noise stemming from inherent stochasticity of the chemical reactions involved in signaling pathways. Cells employ multiple strategies to improve the accuracy by tuning the reaction rates, for instance amplifying the response, reducing the noise etc.. However, the pathway also consumes energy through incorporating ATP in phosphorylating key signaling proteins involved in the reaction pathways. In many instances, improvements in accuracy elicit extra energetic cost. For example, higher deactivation rate suppresses the basal pathway activity effectively amplifying the dynamic range of the response which leads to improvement in accuracy. Higher deactivation rate also enhances the energy dissipation rate. Here, we employed a theoretical approach based on thermodynamics of information to explore the role of accuracy and energetic cost in the performance of a Mitogen Activated Protein Kinase signaling system. Our study shows that the accuracy-energy trade-off can explain the optimality of the reaction rates of the reaction pathways rather than accuracy alone. Our analysis elucidates the role of interplay between accuracy and energetic cost in evolutionary shaping of the parameter space of signaling pathways.