Exploring the Vertex Form of a Parabola
Loading the math board and drawing, please wait…
This example demonstrates the vertex form of a parabola, involving key mathematical concepts such as parabolas, functions, and curve sketching. By adjusting parameters h, k, and a, you can observe changes in the parabola's shape. The example uses GeoGebra objects h, k, a, g, f, A, B, and eq1, suitable for high school mathematics education and learning.
GeoGebra Commands & Parameters
Numeric h(16)Numeric k(-10)Numeric a(0.200000000000003)y = x^(2)f(x) = (a * (x - h)^(2)) + k(h, k)(0, f(0))x = h
AI Drawing Prompt Reference
Draw a parabola with its vertex at point (h, k), where h and k are adjustable parameters. The opening direction is determined by coefficient a: positive a opens upward, negative a opens downward. First sketch the basic parabola y = x² as a reference, then draw the target parabola f(x) = a(x - h)² + k. Mark the vertex point, and draw the vertical axis of symmetry x = h passing through the vertex. Also mark the y-intercept, which is the function value when x = 0. By adjusting h, k, and a, observe how the parabola's shape and position change.
The prompt above was compiled from the original drawing commands and is for reference only.