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Quadratic Equations in Standard Form

Quadratic Equations in Standard Form
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2018-10-04 02:22
FunctionCoordinate Geometry
This example demonstrates the graph of a quadratic equation in standard form, including its roots, vertex, axis of symmetry, and other geometric properties. Key math concepts involved are quadratic functions, roots, vertex, axis of symmetry, and discriminant. The construction uses commands like LaTeX for equations, Root to find roots, If for conditional logic, Polygon for graphing, and Sequence for generating data points, involving objects such as allX, none, c, a, b, theFunction, zero1, zero2, theConic, vertex, equation, yInt, bLabel, cLabel, aLabel, etc. It is suitable for high school mathematics teaching to understand the transformations and properties of quadratic function graphs.

GeoGebra Commands & Parameters

  1. LaTeX("\text{\vphantom{()}none}") → none
  2. Root(theFunction) → zero1, zero2
  3. If(¬(a ≟ 0), Vertex[theConic]) → vertex
  4. LaTeX(("\vphantom{-}b=" * b)) → bLabel
  5. LaTeX(("\vphantom{-}c=" * c)) → cLabel
  6. LaTeX(("\vphantom{-}a=" * a)) → aLabel
  7. Polygon({(-8.5, 12.5), (8.5, 12.5), (8.5, -12.5), (-8.5, -12.5)}) → viewBox
  8. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  9. Zip(theFunction(A), A, xVals) → yVals
  10. Sequence(yVals(i) - yVals(i - 1), i, 2, 5) → firstDiffs
  11. Sequence(firstDiffs(i) - firstDiffs(i - 1), i, 2, 4) → secondDiffs
  12. If(a ≟ 0, none, Text[vertex]) → vertexDisplay
  13. If(a ≟ 0 ∧ b ≟ 0, If[c ≟ 0, allX, none], If[Defined[zero1] ∧ Defined[zero2], LaTeX[x(zero1) + ", " + (x(zero2))], If[Defined[zero1], LaTeX[x(zero1)], none]]) → zeroDisplay

AI Drawing Prompt Reference

Draw the graph of a quadratic function in standard form, showing the parabola, its vertex, axis of symmetry, the two real roots when they exist, and the y‑intercept; label the coefficients a, b, and c beside the plot; display the vertex coordinates when a ≠ 0 and show the root x‑values when the discriminant is non‑negative; set the viewing window roughly from x = -8.5 to 8.5 and y = -12.5 to 12.5.
The prompt above was compiled from the original drawing commands and is for reference only.