This paper presents an approach for global trajectory planning using quadratic optimization and dynamic programming. In the global route planning phase, the goal is to find a route with minimal curvature for any road geometry, while a speed profile is determined by dynamic programming based on the vehicle's dynamic constraints. The method has a low computational cost and is well-suited for integration within a hierarchical system architecture, where the trajectory can be further refined with local route planning to enable the vehicle to adapt to changing environmental conditions. The developed method ensures vehicle stability while achieving the highest possible speed. The approach is implemented in the Frenet coordinate system within a self-developed simulation environment that allows for a comprehensive evaluation of vehicle dynamics, trajectory feasibility, and performance metrics. The results show that the proposed method can generate smooth and dynamically feasible trajectories while balancing curvature minimization, safety, and computational efficiency, making it well-suited for real-world applications.