Lines and Parabolas - Quadratic Polynomials and Geometric Relations

Delve into an advanced exploration of parabolas and quadratic polynomials in this 38-minute mathematics lecture. Learn to compute subderivatives, tangent lines, and Taylor expansions using elementary algebraic calculus. Master the technique of completing the square to analyze the shape and behavior of parabolas, and discover intriguing geometrical relationships related to addition and multiplication. Follow along as the instructor demonstrates graphing techniques, explores the meets of tangents, derives equations for lines between points, and examines the standard parabola and polarity. Engage with practical exercises to reinforce your understanding of these complex mathematical concepts.

Intro to parabolas and quadratic polynomials
Completing the square
Re-writing the polynomial P
Translating and scaling a parabola
Example of graphing a parabola
Meets of tangents of a parabola
The equation of a line between two points
Standard parabola and polarity
Exercises on polarity