Intercept Form Visualized with Geometric Construction

This GeoGebra example visualizes how an intercept form (intercept form) connects geometric features on the coordinate plane—particularly the positions of intercepts/roots—to the graph behavior of a quadratic equation. It centers on key concepts such as intercepts of quadratic functions, identifying x- and y-intercept information from geometric construction, and using perpendicular lines and intersection points to determine the parameters implied by the form. The construction is built with GeoGebra commands Segment and Point to create the geometric scaffolding, OrthogonalLine to draw perpendicular helper lines from reference objects, and Intersect to compute critical intersection points whose coordinates (e.g., x_{1}, y_{1}) represent the needed quantities. Named objects and equations (e.g., eq1, eq2, functions f and g, and text labels) are used to link the algebraic intercept form constraints with the displayed geometry. Suitable for secondary school instruction on functions and equations, and for learners exploring the relationship between analytic expressions and geometric interpretation.