Factored Quartic with Real Roots Visualization

① This example demonstrates a factored quartic polynomial function and highlights the positions of all its real roots on the x-axis. ② Core mathematical concepts include the factored form of quartic functions, the correspondence between real roots and x-intercepts, and the geometric meaning of intersections between the graph and the coordinate axes. ③ Construction details: Based on the summary, the GeoGebra commands involve Intersect, with objects including the function f, four root points r1 through r4, intersection points A, B, C, D, E, and text labels text1 and text2; auxiliary elements such as planes, similarity transformations, cylinders, and triangles may be used to enhance the visual presentation. ④ Suitable for high school or pre-university students learning polynomial functions, factoring, and root relationships, as well as for teachers demonstrating the connection between algebraic expressions and graphs in class or for students' independent exploration.