Geometric Meaning of Coefficients in a Quadratic Function

Draw a parabola representing a quadratic function, and illustrate the geometric meaning of its coefficients. Select two key points on the parabola, draw a vector from one point to the other, then draw another vector from the second point to a point on the parabola, forming a chain of vectors. At a certain point on the parabola, construct a tangent line, and from the point of tangency draw two vectors pointing to two other points on the parabola, to show the relationship between coefficients, the tangent, and the vectors. The final image should include the parabola, the tangent line, multiple vectors with their endpoints, clearly demonstrating the connection between the quadratic coefficients and the geometric elements.