4th Degree Function: Exploring the Geometry and Algebra of Quartic Curves
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数式処理(CAS) を学ぶ
This example demonstrates the graph of a 4th-degree function using GeoGebra, highlighting differences from quadratic and exponential functions. Key mathematical concepts include polynomial functions, graph transformations, and parameter effects. Construction involves objects like f, eq1 to eq5, and s. Suitable for high school students learning function graph transformations and coordinate geometry.
GeoGebra Commands & Parameters
(a * x^(4)) + (b * x^(3)) + (c * x^(2)) + (d * x) + keq1: f(1) = 10eq2: f'(1) = 0eq3: f(4) = -1eq4: f''(4) = 0eq5: f(-3) = 0Solve({eq1, eq2, eq3, eq4, eq5})Substitute(f, s)
AI Drawing Prompt Reference
Draw the graph of a quartic function that satisfies the conditions: it has a value of 10 at x=1, a derivative of 0 at x=1, a value of -1 at x=4, a second derivative of 0 at x=4, and a value of 0 at x=-3. Determine the specific form of the function from these conditions and plot its graph.
The prompt above was compiled from the original drawing commands and is for reference only.