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Graphing the Absolute Value of a Quadratic Function

Graphing the Absolute Value of a Quadratic Function
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2019-03-08 01:17
FunctionCoordinate GeometryGraphing
This example demonstrates how to graph the absolute value of a quadratic function. Key mathematical concepts include quadratic functions and absolute value functions. Using GeoGebra commands such as Flatten, Sequence, and Point, you can dynamically adjust parameters and observe changes in the graph. Suitable for high school mathematics education and learning about quadratic function graph transformations.

GeoGebra Commands & Parameters

  1. Flatten(Sequence[Sequence[(i, j), i, -10, 10], j, 0, 10]) → GridSpace
  2. Sequence((12, i), i, 2, 6, 2) → homeSpace
  3. Point(Union[GridSpace, {Element[homeSpace, 1]}]) → P_1
  4. Point(Union[GridSpace, {Element[homeSpace, 2]}]) → P_2
  5. Point(Union[GridSpace, {Element[homeSpace, 3]}]) → P_3
  6. Random(-10, 4) → Root1
  7. Random(1, floor(maxAval)) → aVal
  8. Expand(((aVal * (x - Root1)) * (x - Root2))) → f
  9. UnicodeToLetter(10007) → xmark
  10. UnicodeToLetter(10003) → cmark
  11. Polygon({bottomLeft, (x(bottomLeft), y(topRight)), topRight, (x(topRight), y(bottomLeft))}) → viewbox
  12. Point(Union[GridSpace, homeSpace]) → ActivePoint
  13. LaTeX(ActivePoint) → activePtLbl
  14. LaTeX(Expand[f]) → Lblf
  15. LaTeX((("\text{Consider \(y=" * Lblf) * "\). Factoring, we get:}")) → fbLine2
  16. LaTeX((("\text{\(" * Factor[f]) * "\)}")) → fbLine4
  17. LaTeX(((("\text{\(" * Lblf) * "=") * If[aVal ≠ 1, (((((("" * aVal) * "(") * Expand[((x - Root1) * (x - Root2))]) * ")\)\\\phantom{") * Lblf) * "}="), "\)}"])) → fbLine3
  18. LaTeX((("\text{From this factored form, we conclude that the \\graph of \(y=" * f) * "\):}")) → fbLine5
  19. UnicodeToLetter(8226) → bullet
  20. LaTeX((((((("\text{\hphantom{12}" * bullet) * " has zeros \(") * Root1) * "\) and \(") * Root2) * "\),\\}")) → fbLine6
  21. LaTeX((((("\text{\hphantom{12}" * bullet) * " has axis of symmetry \(x =") * xCoordVertex) * "\), and}")) → fbLine7
  22. LaTeX((("(" * xCoordVertex) * ")")) → subStr
  23. IndexOf("x", Lblf) → firstX
  24. If(Defined[firstX], IndexOf["x", Take[Lblf, firstX + 1]] + firstX) → secondX
  25. LaTeX(If[Defined[firstX], (Take[Lblf, 1, firstX - 1] * subStr), ""]) → subFirstX
  26. LaTeX((subFirstX * If[Defined[secondX], (Take[Lblf, firstX + 1, secondX - 1] * subStr), Take[Lblf, firstX + 1]])) → subSecondX
  27. LaTeX((subSecondX * If[Defined[secondX] ∧ secondX < Length[Lblf], Take[Lblf, secondX + 1], ""])) → subComplete
  28. LaTeX("") → fbLine1
  29. LaTeX((((((("\text{\hphantom{12}" * bullet) * " \(y_\text{vertex}=") * subComplete) * "=") * yCoordVertex) * "\) is the \\ \(y\)-coordinate of the vertex.}")) → fbLine8
  30. Sequence((("SetFixed(P_" * i) * ",false,false)"), i, 1, 3) → test
  31. LaTeX((((((((("\text{Therefore, the vertex is \((" * xCoordVertex) * ",") * yCoordVertex) * ")\), which maps to\\\((") * xCoordVertex) * ",") * abs(yCoordVertex)) * ")\) on \(y= \left\vert f(x) \right\vert\) .}")) → fbLine9
  32. LaTeX((((((((((((((((fbLine1 * "\\") * fbLine2) * "\\") * fbLine3) * fbLine4) * "\\") * fbLine5) * "\\") * fbLine6) * "\\") * fbLine7) * "\\") * fbLine8) * "\\") * fbLine9)) → fbComplete
  33. LaTeX((((("\text{\textbf{Question: }" * MainInstruc) * "\\\textbf{Instructions: }") * SpecInstruc) * "}")) → allInstruc

AI Drawing Prompt Reference

Draw the absolute value of a quadratic function. First, create a grid, then place three points on the grid representing the roots and vertex of the quadratic function. Randomly generate an a value and one root, then calculate the other root. Use these roots to construct the quadratic function and display its expanded form. Next, find the coordinates of the vertex and determine its corresponding point on the absolute value function graph.
The prompt above was compiled from the original drawing commands and is for reference only.