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Quadratic Equations with the Square Roots Method: Build and Check

Quadratic Equations with the Square Roots Method: Build and Check
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2024-03-09 19:03
FunctionInequalityGraphing
This GeoGebra example demonstrates how to solve quadratic equations using the properties of equality and the square roots method, with interactive inputs and built-in answer validation. It focuses on core ideas such as transforming a quadratic equation step-by-step, handling the ± outcome when taking square roots, and ensuring the generated coefficients produce solvable cases. The construction uses randomized problem generation (RandomUniform, Sequence, Take, KeepIf, Element, Zip, TableText) and conditional logic (If) to select valid parameters and control difficulty. For presentation and interaction, it includes on-screen text and input fields (Text, Textfield, onboardingTextOffset), interface layout elements (Polygon, Corner, Text), and positioning via Translate, while solution display and user feedback are driven by objects and state controls (validA/validB/validC, showanswer/showsolution, btnValidate/btnNew, showhint, and input variables). Suitable for grades 9–12, classroom practice, and student self-study on quadratic equation solving techniques.

GeoGebra Commands & Parameters

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.19312275996991282, 0.9142319732126456, 0.5357229655159863, 0.46165332883546906, 0.054278039609244065, 0.9070762791064417, 0.7491949226108137, 0.03873295336436259, 0.41065165499960377, 0.10153507501562387, 0.739352503760725, 0.8751485518929651, 0.292389011195522, 0.05874952888251355, 0.017072191947286278, 0.8527563200745021, 0.7619984498772734, 0.06761391268901312, 0.9046320608842139, 0.11328331093635712, 0.06394488125667078, 0.6450567460592029, 0.03310800838302324, 0.18237475494968539, 0.49868457723166953, 0.35174947700904013, 0.304371941888673, 0.17808111295966525, 0.9890776619883722, 0.564565932027976, 0.013319384400723357, 0.13010333870845125, 0.12679283318059315, 0.6382771434930309, 0.38297451385739445, 0.3183698080516357, 0.5681839348375627, 0.6598165802922142, 0.8093309035172046, 0.2164625197916744, 0.8431708903628095, 0.0689873612977044, 0.8341816660156295, 0.6070405674026742, 0.7868974970407153, 0.6497078010329836, 0.2727771109049204, 0.6927273658188717, 0.2323666117471265, 0.705804017684031, 0.8389195605851376, 0.1369340438094627, 0.6628682146554976, 0.6449572191014923, 0.6730638538858479, 0.5747846917522906, 0.4858187120343723, 0.0037014902890436297, 0.7491385804516398, 0.744689934369749, 0.504620217685367, 0.6553413202231987, 0.31313684896474386, 0.9361839470058462, 0.11232591884800534, 0.9613211670986243, 0.7410474602593623, 0.6893955639096968, 0.3602631371663904, 0.6449284844682517, 0.1454057115003477, 0.4859676146546611, 0.7463184829481558, 0.5542486307635208, 0.13863963234518278, 0.5803697014602107, 0.13132949768762736, 0.9690154776621979, 0.0074722336306913125, 0.40436739591424, 0.5179550790237092, 0.4634122502722461, 0.3659103389381583, 0.5359175159915409, 0.16451212011193211, 0.303978396381169, 0.9248111244228693, 0.016951778147458865, 0.14656874714321316, 0.20856404469974696, 0.8736630362339516, 0.47239236002127244, 0.3915744783187946, 0.30874884458155827, 0.47505168069221126, 0.77531117843158, 0.6464853811119273, 0.364304130003255, 0.4043036048895637, 0.8204006044762187, 0.2952080048814964, 0.7641266104231677, 0.1360088163673835, 0.6198664748496435, 0.49173786061019115, 0.22360926690869032, 0.3655203245901319, 0.22248545683379245, 0.24610919361122996, 0.8636394664382636, 0.2271120442396287, 0.6478868888801237, 0.33369976854884026, 0.2613266217050107, 0.40124879845600514, 0.8741253147005701, 0.054050501256531235, 0.7971611476993541, 0.8713805503057558, 0.7173030531774298, 0.8431616061149764, 0.19759372268259195, 0.2558195120270889, 0.7373831843156763, 0.723217977427497, 0.9859984630614896, 0.9225931241928098, 0.4644015600405024, 0.28587341006344874, 0.5386454953747098, 0.49468702819080274, 0.6140425759912875, 0.7995895143920156, 0.5356585129950803, 0.9098011670108542, 0.680986345417223, 0.6680768101206218, 0.8699693372099867, 0.8326389969876525, 0.8525661773195622, 0.7256267712067527, 0.6800068289396077, 0.4588332229505822, 0.2440934766566588, 0.8460503056625176, 0.30426906310234997, 0.017883413703001866, 0.33071298907306146, 0.15505444992395265, 0.42802747407889913, 0.6979396173998526, 0.86884475048938, 0.78119085116643, 0.7841988964925329, 0.47791263610241147, 0.7031499959696523, 0.15800033976446326, 0.5818959425965669, 0.6222255225025943, 0.5225264112852558, 0.7796556697435194, 0.3273281234614995, 0.3905425868430544, 0.3408943596480211, 0.714269416066077, 0.8625760079534006, 0.39902083378015957, 0.14547868373588269, 0.5930870965845704, 0.17829769507093954, 0.6410255412774551, 0.2569218445971265, 0.9700255500430202, 0.866651202347747, 0.09383551066193091, 0.06188224560918223, 0.5344444970196904, 0.580629343918699, 0.9136350078188832, 0.009777737300486377, 0.0806543595761513, 0.9756019377552411, 0.3640485358869457, 0.33102741586014406, 0.08046631918675093, 0.7181486402097095, 0.0036209461870775526, 0.4345258586975046, 0.6700803956420344, 0.5762394006494891, 0.034979242512316856, 0.7271521173605774, 0.5697858023080383, 0.8034821919026146, 0.8329342068834492, 0.5978718933423606, 0.35431224623297164, 0.10850679561165133, 0.570489052849089, 0.24343444116437207}
  2. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  3. Sequence(-3, 3) → coeffbs
  4. KeepIf(IsInteger[sqrt(kk - coeffb)], kk, Sequence[-9, 9] \ {0}) → coeffcs
  5. Element(coeffcs, Mod[countQuestion, 1 + floor((currentRandomSeeds(4) * Length[coeffcs]))] + 1) → coeffc
  6. Element(coeffds, 1 + floor((currentRandomSeeds(5) * Length[coeffds]))) → coeffd
  7. Polynomial((coeffa * x^(2))) → level2Eq
  8. Polynomial((coeffa * x^(2)) + coeffc) → level3Eq
  9. If(coeffa ≟ 1, (x + coeffd)^(2) + coeffc, coeffa ≟ -1, (-(x + coeffd)^(2)) + coeffc, (coeffa * (x + coeffd)^(2)) + coeffc) → level4Eq
  10. Element({level1Eq, level2Eq, level3Eq, level4Eq}, randomLevel) → equat
  11. Zip(x(PP), PP, RemoveUndefined[rootsPoints]) → sols
  12. Zip((If[kk ≥ 0, "", "-"] * FractionText[abs(kk)]), kk, sols) → solsText
  13. If(randomLevel ≟ 1, 1, coeffa) → a
  14. If(randomLevel ≟ 4, coeffd, 0) → d
  15. If(randomLevel ≥ 3, coeffc, 0) → c
  16. If(randomLevel ≟ 1, coeffn, coeffb) → b
  17. KeepIf(Length[ll] ≟ 3, ll, {l1, If[c ≟ 0, {}, l2], If[a ≟ 1, {}, l3], If[Length[sols] ≟ 0 ∨ b - c ≟ 0, {}, l4], If[Length[sols] ≟ 0, {}, l5], If[Length[sols] ≟ 0 ∨ d ≟ 0, {}, l6]}) → l7
  18. TableText(l7, "rcl") → workedSol
  19. Textfield(inputB) → InputBoxB
  20. Zip((("$\textsf{" * tt) * " }$"), tt, {"Choose an option", "No real solutions", "One real solution", "Two real solutions"}) → menu
  21. Take({correct1, correct2, correct3}, 1, 1 + Length[sols]) → corrects
  22. Polygon(Zip[PixelsToPoint[Corner[1], Corner[3], Corner[5], A], A, {(pixelsLeft, pixelsTop), (pixelsLeft, y(Corner[5]) - pixelsBottom), Corner[5] - (pixelsRight, pixelsBottom), (x(Corner[5]) - pixelsRight, pixelsTop)}]) → borderBox
  23. Corner(5) → layoutAppSize
  24. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  25. Textfield(inputA) → InputBoxA
  26. Textfield(inputC) → InputBoxC
  27. TableText(Text[equat], "=", Text[If[randomLevel ≟ 1, coeffn, coeffb]], "lcr") → textequation
  28. Text(textequation, (0, 0), true, true, 0, 0) → textequationPos
  29. Translate(f, Vector[(Vector[Corner[1], Corner[4]] / 500 * 24)]) → f'
  30. Translate(If[correct1, pic1, pic2], Vector[B, D]) → pic3
  31. Translate(If[correct2, pic1, pic2], Vector[B, E]) → pic4
  32. Translate(If[correct3, pic1, pic2], Vector[B, F]) → pic5

AI Drawing Prompt Reference

Create an interactive quadratic equation learning interface with a main text area displaying the quadratic equation, three input boxes below for entering a, b, c coefficients, and a selection menu on the right or below for users to choose the number of real solutions (no real solutions, one real solution, two real solutions). Include a step-by-step solution table showing the simplification and solving process, with a validation button to check answer correctness. The overall layout uses a rectangular border as container background with elements reasonably distributed to form a clear educational tool interface.
The prompt above was compiled from the original drawing commands and is for reference only.