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Draw Parabola Given Vertex and Point (Quadratic Function)

Draw Parabola Given Vertex and Point (Quadratic Function)
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2013-03-07 04:27
FunctionCoordinate GeometryGraphing
In collections Geom. & Alg.: Quadratics
This example demonstrates how to draw a parabola's graph using its vertex and a point. It involves core math concepts like quadratic functions, vertex form equations, and coordinate geometry. Key GeoGebra commands used include vertex, A, a, and f. Suitable for high school students learning quadratic functions and analytical geometry.

GeoGebra Commands & Parameters

  1. Point vertex(1.0, 1.0)
  2. Point A(4.74, 1.6)
  3. (y(A) - y(vertex)) / (x(A) - x(vertex))^(2)
  4. f(x) = a * (x - x(vertex))^(2) + y(vertex)

AI Drawing Prompt Reference

Draw a parabola using its vertex and a point on the curve, showing how to determine the equation and graph from the vertex coordinates and another point's coordinates, first marking the vertex and the other point, then calculating the square of the slope from the coordinates difference, and finally writing the parabola equation with the vertex coordinates and calculated slope square value to plot the graph.
The prompt above was compiled from the original drawing commands and is for reference only.