Graphing Cubic Equations
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This example demonstrates how to graph cubic equations. It involves core mathematical concepts such as functions, equations, and coordinate geometry. Key construction elements include using GeoGebra commands and objects like a, b, c, d, f_1, Maxi, Mini, f_2, f_3, yvalue, n, button1, text1, text2, text3, f_4, text4 to create and manipulate the graphs. Suitable for high school students and teachers for teaching and exploring the properties of cubic functions.
GeoGebra Commands & Parameters
Numeric a(0.1)Numeric b(-4)Numeric c(1)Numeric d(5)f_1(x) = (((a * (x - b)) * (x - c)) * (x - d))y(Max[f_1, b, d])y(Min[f_1, b, d])f_2(x) = ((a * (x - b)) * (x - c)^(2))f_3(x) = (a * (x - b)^(3))abs(Max[abs(Maxi), abs(Mini)])Numeric n(1)f_4(x) = ((a * (x - b)) * (x^(2) + (b * x) + b^(2) / 4 + 1))
AI Drawing Prompt Reference
Draw a cubic function graph, including f1(x) = ((0.1 * (x + 4)) * (x - 1) * (x - 5)), and its maximum and minimum points. Then draw f2(x) = ((0.1 * (x + 4)) * (x - 1)^2) and f3(x) = (0.1 * (x + 4) * (x - 1)^3), and finally f4(x) = ((0.1 * (x + 4)) * (x^2 + (4 * x) + 5)), to observe their shapes and characteristics.
The prompt above was compiled from the original drawing commands and is for reference only.