Exploring Absolute Value Equations: Effects of Parameters a, h, k on V-shaped Gr

①This interactive GeoGebra file demonstrates how the graph of y=a|x-h|+k changes as parameters a, h, and k are varied, revealing the connection between absolute value equations and V-shaped parabolas. ②Core mathematical concepts include absolute value functions, vertical/horizontal translations, vertical stretching/compression, and the role of the vertex (h,k) in determining the graph's position and shape. ③Construction details: The file uses Point commands to create key points, sliders for parameters a, h, and k, and functions f and g to plot the graphs. Text objects (text1, text2, text3) display the current parameter values and the equation, enabling dynamic exploration. ④Suitable for middle school to high school students learning function transformations, as well as for classroom demonstrations or self-study, fostering visual and interactive understanding of algebraic concepts.