With the ongoing advancement of video technology and the emergence of new video platforms, suppliers of video contents are striving to ensure that the video quality meets the desire of consumers. Accessing a limited amount of channel bandwidth, they are often looking for a novel approach to decrease the use of data and thus the required energy and cost. This study evaluates the Quality Rate performance of H.264, H.265, and VP9 codecs across resolutions (960*544, 1920*1080, 3840*2160) to optimize video quality while minimizing bitrate, crucial for energy and cost efficiency. At this approach, original videos at native resolutions were encoded, decoded, and rescaled using FFmpeg. For each resolution, encoding and decoding were performed at various quantization levels. Quality Rate (QR) curves were generated using PSNR and VMAF metric against bitrate. Convex Hull curves were then derived and mathematically modelled for each resolution. The procedure was systematically applied to H.264, H.265, and VP9 codecs. Results indicate that increasing CRF values reduce bitrate, PSNR, and VMAF, with PSNR ranging between 20-40 dB. Logarithmic polynomial modelling of convex hulls demonstrated high accuracy, with low RMSE and high R-Squared values. These findings suggest that the convex hull of one codec can predict the performance of others, aiding future content-driven prediction methodologies and enhancing adaptive streaming efficiency. Keywords: Video Codecs, Adaptive Streaming, Compression, Bitrate, PSNR, VMAF, H.264, H.265, VP9