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Vertex Form of Parabolas

Vertex Form of Parabolas
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2015-11-26 03:04
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the vertex form of a parabola, a(x-h)²+k. Key mathematical concepts include the properties and transformations of parabolas. By adjusting the values of a, h, and k, one can observe changes in the vertex, direction of opening, and axis of symmetry. Commands used include Extremum, Intersect, Polygon, etc. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Extremum(f) → A
  2. Intersect(f, xAxis) → B, C
  3. Polygon((1.5, -1), (1.5, y(Corner[2])), Corner[2], (x(Corner[2]), -1)) → poly1, d, e, h_1, i
  4. Simplify(f) → g
  5. Text("y-intecept: D(0," + (f(0)) + ")") → yIntercept
  6. If((y(A) ≠ 0) ∧ (¬Defined[B]), "There are NO x-Intercepts", If[(x(B) ≠ 0) ∨ (x(C) ≠ 0) ∧ Defined[C], "The x- intercepts are B" + B + " and C" + C, "The x-intercept is B" + B]) → xIntercepts
  7. TableText({{"", "", "Chart"}, line1, line2}, "|_c") → chart