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Finding Quadratic Equation Roots Graphically

Finding Quadratic Equation Roots Graphically
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2023-09-04 18:48
FunctionGeometric ConstructionGraphing
This activity demonstrates how to find the roots of a quadratic equation by graphing. The key mathematical concepts involve the relationship between quadratic equations and their function graphs. Construction uses GeoGebra commands like Polynomial, Segment, and PointToPixels to create the quadratic function and coordinate points. Suitable for students in grades 9-12 for algebraic practice.

GeoGebra Commands & Parameters

  1. Shuffle(Sequence[A / 100, A, 0, 100]) → allRandomSeeds, {0.26, 1, 0.33, 0.95, 0.89, 0.17, 0.14, 0.03, 0.92, 0.76, 0.56, 0.68, 0.11, 0.19, 0.22, 0, 0.13, 0.99, 0.07, 0.43, 0.74, 0.93, 0.12, 0.81, 0.59, 0.82, 0.94, 0.36, 0.6, 0.58, 0.4, 0.62, 0.7, 0.52, 0.38, 0.35, 0.29, 0.72, 0.9, 0.34, 0.91, 0.53, 0.46, 0.75, 0.18, 0.84, 0.61, 0.79, 0.23, 0.1, 0.16, 0.08, 0.88, 0.2, 0.25, 0.65, 0.67, 0.86, 0.45, 0.98, 0.5, 0.66, 0.39, 0.42, 0.78, 0.28, 0.32, 0.05, 0.8, 0.73, 0.55, 0.41, 0.69, 0.04, 0.37, 0.97, 0.71, 0.24, 0.01, 0.54, 0.85, 0.49, 0.63, 0.09, 0.77, 0.48, 0.3, 0.44, 0.47, 0.64, 0.21, 0.51, 0.31, 0.15, 0.02, 0.06, 0.27, 0.87, 0.83, 0.57, 0.96}
  2. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  3. If(currentRandomSeeds(3) ≤ 0.2, 0, If[currentRandomSeeds(3) ≤ 0.6, 1, 2]) → NumOfSols
  4. If(-4 + floor((currentRandomSeeds(2) * 8)) ≠ 0, -4 + floor((currentRandomSeeds(2) * 8)), 1) → yV
  5. KeepIf(abs(x) ≥ abs(yV) / (5 - abs(xV))^(2), Sequence[-5, 5] \ {0}) → coeffsA
  6. Element(coeffsA, Mod[floor((currentRandomSeeds(3) * 10)), Length[coeffsA]] + 1) → coeffA
  7. Sequence(xA + (0.5 * ii), ii, 1, Min[10 - (2 * xA), 6]) → xBPos, {-2.5, -2, -1.5, -1, -0.5, 0}
  8. Element(xBPos, xBind) → xB
  9. KeepIf(abs(x) ≤ 20 / (xB - xA)^(2), Sequence[-4, 4, If[Mod[Denominator[(xA * xB)], 2] ≟ 0 ∨ Mod[Denominator[xA + xB], 2] ≟ 0, 2, 1]] \ {0}) → coeffsA2
  10. Element(coeffsA2, Mod[floor((currentRandomSeeds(3) * 10)), Length[coeffsA2]] + 1) → coeffA2
  11. Zip((("$\textsf{" * tt) * " }$"), tt, options) → menu
  12. SelectedIndex(menu) → selectedOption
  13. Polynomial(Element[{g0, g1, g2}, NumOfSols + 1]) → g
  14. RemoveUndefined({Root[g]}) → sols
  15. If(Length[sols] ≥ 2, (abs(input2 - x(sols(1))) ≤ 0.1 ∨ abs(input2 - x(sols(2))) ≤ 0.1) ∧ input2 ≠ input1, ¬Defined[input2]) → correct3
  16. If(Length[sols] ≥ 1, abs(input1 - x(sols(1))) ≤ 0.1 ∨ abs(input1 - x(sols(2))) ≤ 0.1, ¬Defined[input1]) → correct2
  17. Take({selectedOption, input1, input2}, 1, selectedOption - 1) → inputCurrent
  18. Textfield(input1) → InputBox1
  19. Textfield(input2) → InputBox2
  20. Corner(5) → layoutAppSize
  21. sectorPixels(A, B, C, haloPixels + 40, Corner[1], Corner[3], Corner[5]) → pulsingObject
  22. sectorPixels(A, B, C, 40, Corner[1], Corner[3], Corner[5]) → displayAngle
  23. PointToPixels(Corner[onboardingDisplayText, 2], Corner[1], Corner[3], Corner[5]) → layoutOnboarding
  24. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  25. Polygon({(-5.5, -5.5), (5.5, -5.5), (5.5, 5.5), (-5.5, 5.5)}) → q1
  26. LaTeX(g, true, true) → text1
  27. Segment((-5.42, 0), (5.415, 0)) → h
  28. Segment((0, -5.42), (0, 5.42)) → i
  29. Text("\math{x}", (5.75, 0.075), true, true, 0, 0) → labelx
  30. Text("\math{y}", (0, 5.9), true, true, 0, 0) → labely
  31. Translate(p, Vector[(Vector[Corner[1], Corner[4]] / 500 * 16)]) → p'
  32. Element({348, 282, 284, 300}, selectedOption) → xFB1
  33. Text(sols(2), sols(2), true, true, 1, If[If[NumOfSols ≟ 2, coeffA2 ≥ 0, coeffA ≥ 0], -1, 1]) → label2
  34. Text(sols(1), sols(1), true, true, If[NumOfSols ≟ 1, 0, -1], If[If[NumOfSols ≟ 2, coeffA2 ≥ 0, coeffA ≥ 0], -1, 1]) → label1
  35. Sequence(Segment[(ii, -0.05), (ii, 0.05)], ii, -5, 5, 0.5) → l1

AI Drawing Prompt Reference

Draw a parabola that opens upwards and intersects the x-axis at two points. Label the x-axis and y-axis, and mark the points where the parabola intersects the x-axis.
The prompt above was compiled from the original drawing commands and is for reference only.