Visualizing Parabola Arc Length with Dynamic Segments

This example demonstrates how to measure and visualize the arc length along a parabola by using a segmented approximation along the curve. It focuses on key ideas of arc-length measurement, curve approximation with a polyline, and working with function graphs—especially quadratic functions—over an interval [a, b]. The construction uses GeoGebra commands Point, Min, Max, Sequence, and PolyLine: f defines the parabola; A and B set the interval endpoints; n controls how many segments are used; a and b are the chosen bounds. Min/Max help determine the correct ordering via minab and maxab. The objects s and l1 represent arc-length-related quantities (such as accumulated segment length or a comparison value), while g is used to display or manage the resulting visualization. Suitable for secondary enrichment and introductory university prep, particularly for building intuition that leads to the calculus arc-length integral.