Translating a Parabola
Loading the math board and drawing, please wait…
This example demonstrates the translation of a parabola by changing parameters p, h, and k. It involves core math concepts like parabola equations, parametric equations, and coordinate geometry. Construction highlights the use of GeoGebra commands/objects: p, A, h, k, c, VERTEX, C, d, Vertex. Suitable for high school students learning function graph transformations.
GeoGebra Commands & Parameters
Numeric p(3)(0, p)Numeric h(0)Numeric k(10)y = (1 / ((4 * p)) * (x - h)^(2)) + k(h, k)(h, k + p)y = (1 / ((4 * p)) * x^(2))Point Vertex(0, 0)
AI Drawing Prompt Reference
Draw a parabola with vertex at (0, 10) and demonstrate the translation of the parabola by changing parameters p, h, and k. Start by plotting the original parabola y = x², then draw a vertical line segment at (0, 10) to mark the vertex. Adjust the vertex position based on the value of p to show the translated parabola. Finally, label the key points (0, 10) and (0, 10+p) on the coordinate system and clearly display the comparison between the original and translated parabolas.
The prompt above was compiled from the original drawing commands and is for reference only.