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Parabolas: Completing the square

Parabolas: Completing the square
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2021-08-04 15:54
FunctionCoordinate Geometry
In collections MATH1052-edX
This example demonstrates how to complete the square to transform a quadratic function into a standard parabola equation. Key mathematical concepts include quadratic functions, completing the square, and parabola properties. Construction involves GeoGebra commands like Coefficients, If, LaTeX, and Textfield to create the parabola graph. Suitable for high school students learning quadratic function properties and coordinate geometry applications.

GeoGebra Commands & Parameters

  1. Coefficients(F) → Lc
  2. If(Element[Lc, 2] ≟ 0, (Element[Lc, 1] * x^(2)) + Element[Lc, 3], (Element[Lc, 1] * x^(2)) + (Element[Lc, 2] * x) + Element[Lc, 3]) → f
  3. LaTeX(f, true, true) → text1
  4. Textfield(usera) → InputBox1
  5. Textfield(userh) → InputBox2
  6. Textfield(userk) → InputBox3
  7. If(usera ≟ a ∧ userh ≟ h ∧ userk ≟ k, 0, If[usera ≠ a ∧ userh ≟ h ∧ userk ≟ k, 1, If[usera ≟ a ∧ userh ≠ h ∧ userk ≟ k, 2, If[usera ≟ a ∧ userh ≟ h ∧ userk ≠ k, 3, If[usera ≠ a ∧ userh ≠ h ∧ userk ≟ k, 12, If[usera ≠ a ∧ userh ≟ h ∧ userk ≠ k, 13, If[usera ≟ a ∧ userh ≠ h ∧ userk ≠ k, 23, 123]]]]]]) → b

AI Drawing Prompt Reference

Draw a parabola with vertex at (h, k) and direction of opening determined by a. First, input the values of a, h, and k, then construct the parabola equation f=ax^2+bx+c based on these values. If the input values of a, h, and k are the same as before, display the parabola equation; otherwise, adjust the position and direction of the parabola based on the new input values.
The prompt above was compiled from the original drawing commands and is for reference only.