Exploring the Derivative of a Quadratic Function

Draw a coordinate plane with two parabolas, one opening upward and one downward, representing positive and negative quadratic functions. Mark points at integer x-coordinates from -4 to 3 on the horizontal axis, and at each corresponding point on the parabolas, draw tangent lines whose slopes indicate the derivative. Use dashed segments to connect symmetric points, forming a rectangular outline, and add axis tick marks. Place a table beside the graph listing x-values, y-values, and tangent slopes for each point, with the table content updating dynamically based on a slider, and include a text note explaining the geometric meaning of the derivative.