Using the following Geogebra template insert three sliders, a, h, and k. In the input field type the general form of the quadratic formula[math] f(x) = a (x-h)^2+k[/math] Insert a dynamic text that displays the formula on the template Adjust sliders until parabola approximately matches Insert points at each pink ball In the input screen do a regression analysis of the quadratic with fitpoly[[i]list points separated by comas, degree of polynomial[/i]] Because of the geometry involved in taking the photograph this is not perfect. [color=#c51414]This template is used to show teachers how to set up sliders and dynamic formulas.[/color]
Hopefully this shows a small bit of the power of Geogebra and the utility of Geogebratube in sharing files.