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Standard Form of Parabolas

Standard Form of Parabolas
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2015-11-26 02:53
FunctionCoordinate GeometryOptimization
This example demonstrates the standard form of a parabola, ax² + bx + c. By adjusting the values of a, b, and c, you can observe changes in the direction of the parabola's opening, its vertex, and its intersections with the coordinate axes. Commands used include Extremum, Intersect, Simplify, Text, If, and TableText, suitable for high school mathematics education.

GeoGebra Commands & Parameters

  1. Extremum(f) → A
  2. Intersect(f, xAxis) → B, C
  3. Simplify(f) → g
  4. Text("y-intecept: D(0," + (f(0)) + ")") → yIntercept
  5. 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
  6. TableText({{"", "", "Chart"}, line1, line2}, "|_c") → chart