Parabola Transformations

Loading the math board and drawing, please wait…

2020-05-05 08:08

This example demonstrates transformations of the parabola, involving key mathematical concepts such as geometric transformations and function graphs. Using GeoGebra commands like TextField, Extremum, Intersect, etc., it dynamically shows the translation and dilation of the parabola. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

Textfield(a) → InputBox1
Textfield(k) → InputBox2
Textfield(h) → InputBox3
Extremum(f) → C
Intersect(f, yAxis) → D
Root(B1) → B
Extremum(B1) → F
Intersect(B1, yAxis) → G
Point(B1) → M0
Vector(M0, M1) → Transform_h
Vector(M1', M2') → Transform_a
Vector(M2', M1') → Transform_{kk}
Vector(M2, M3) → Transform_k
Root(f) → A, E

AI Drawing Prompt Reference

Draw a parabola y=x^2, then adjust its translation and stretching using input boxes. First, enter the translation amount h to translate the parabola; then enter the stretching coefficient k to stretch the parabola; finally, enter the angle a to rotate the parabola. Show the parabola's vertex, its intersection with the y-axis, and the key transformation vectors.

The prompt above was compiled from the original drawing commands and is for reference only.