Explore the concept of quadratic curvature for algebraic curves in this differential geometry lecture. Extend the discussion of curvature from parabolas to more general conics and algebraic curves. Discover the advantages of basing curvature on parabolas, including connections to foci and applications to studying surfaces in three-dimensional space. Delve into formulas that allow for easy transitions between different viewpoints, appreciating their power in defining the subject. Learn about the usefulness of considering the square of the usual curvature, which can be formulated without square roots. Gain insights into this important aspect of differential geometry, laying the groundwork for understanding more complex geometric concepts.