Multiples of Functions Have the Same Roots: Geometric Construction and Coordinat

This Geogebra example illustrates that multiplying a function by a scalar does not change its roots. The key mathematical concepts involve function roots, scalar multiplication, and geometric transformations in coordinate geometry. The construction uses the Intersect command and objects like c_1, d, e, r_1, r_2 to determine intersections. This example is suitable for high school or university students learning function properties and geometric constructions.