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Manipulating Parabolas in Vertex Form

Manipulating Parabolas in Vertex Form
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2012-09-25 06:34
FunctionCoordinate GeometrySlider AnimationGraphing
① This example demonstrates dynamic manipulation of a parabola using its vertex form. ② Core concepts include the quadratic vertex form y = a(x‑h)² + k, parabola orientation, vertex coordinates, and scaling/translation transformations. ③ Construction highlights: sliders for parameters a, h, k control the coefficient and vertex; point c represents the vertex (h,k); object d serves as an auxiliary point or focus; text1 displays the live equation. ④ Suitable for high‑school algebra, pre‑calculus, and classroom exploration of function graphs.

GeoGebra Commands & Parameters

  1. Conic c
  2. Numeric h(2.0)
  3. Numeric k(1.0)
  4. Numeric a(1.0)
  5. y = a * (x - h)^(2) + k

AI Drawing Prompt Reference

Draw a parabola in vertex form y = a(x - h)^2 + k, with sliders controlling the coefficient a and the vertex coordinates (h, k). Show the vertex as a point at (h, k) and include an auxiliary point representing the focus for reference. The graph updates dynamically as the sliders move, illustrating scaling, translation, and orientation changes. Display the current equation in text on the screen. This visual setup is ideal for high‑school algebra and pre‑calculus lessons, allowing students to explore how changes in a, h, and k affect the shape and position of the parabola.
The prompt above was compiled from the original drawing commands and is for reference only.