Traffic flow prediction is crucial for managing traffic, reducing pollution, ensuring public safety, and is a vital element of Intelligent Transportation Systems. Furthermore, the variables that influence traffic patterns (such as public events, road closures, and accidents) are predominantly unforeseen, rendering the prediction of traffic flow an intricate undertaking. The objective of this research is to enhance the accuracy of traffic flow forecast by employing a novel strategy that utilizes feedforward Neural-Networks and the Quasi-Newton method for optimization. The proposed strategy decreases the error factor based on the Lagrange multiplier and Jacobian vector. This enhancement has resulted in expedited convergence throughout the process of learning. The sample was chosen using datasets provided by the Traffic Monitoring System, specifically from Highway England, Performance Measurement System, and Maryland 511, for the year 2023. In order to assess the proposed model, the research outcomes are juxtaposed with other established prediction methodologies. The study revealed that the research model that was established performed better than previous prediction strategies based on measures of mean absolute error and root mean squared error.