Edit Function Expression to Match Locus of a Constrained Point

This interactive GeoGebra example presents a task where students must edit the algebraic expression of a function so that its graph matches the locus of a constrained point. The core mathematical concepts involve function graphs, loci, constraints, and the correspondence between algebraic forms and geometric representations. The construction uses GeoGebra commands: Point to create the constrained point A, Textfield to provide an input box (inputBox1), and objects including function c, point A, function f, and the input box. Students modify the expression in the input box to adjust function f until its curve aligns with the locus traced by point A. This activity is suitable for high school or early college students, reinforcing understanding of function transformations, algebraic manipulation, and geometric visualization.