Completing the Square in GeoGebra: From Quadratic Form to Vertex Form

This GeoGebra practice demonstrates how completing the square converts a quadratic expression from a general form into a vertex (standard) form, making the geometry of the parabola easier to read—especially the vertex location and axis of symmetry. The key mathematical concepts include algebraic equivalence by completing the square, expansion and recombination of squares (e.g., turning x^2+bx into (x+b/2)^2−(b/2)^2), and interpreting parameters through the graph of a quadratic function. Construction-wise, the typical workflow is to enter the original quadratic and then input the completed-square (vertex-form) expression as an algebraic function in GeoGebra; the corresponding function graph and related geometric objects (vertex point, symmetry line, and intercepts) update automatically to reflect the transformation. Since the provided source contains no explicit GeoGebra commands or object list, the construction should rely on algebra-to-graph linking: build the completed-square form in the Algebra view and compare its graph with the original. Suitable for secondary school through early undergraduate courses, particularly for teaching and practicing completing the square and connecting algebraic manipulation with geometric interpretation.