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Solve Quadratic Equation Using Formula

Solve Quadratic Equation Using Formula
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2014-07-18 04:40
FunctionCoordinate GeometryComplex NumberOptimization
In collections UCSS Secondary Math II Unit 3B Lesson 2
This example demonstrates solving the quadratic equation 2x^2 + 9 = –8x using the quadratic formula and verifying the solutions. It covers core concepts like quadratic equations, the quadratic formula, discriminant, and the relationship between function graphs and roots. The construction involves GeoGebra commands/objects such as GCD, Polygon, Line, Simplify, PrimeFactors, Unique, Length, Sequence, Product, If, Textfield, ComplexRoot. Suitable for high school mathematics education to understand quadratic equation solving and graphical interpretation of roots.

GeoGebra Commands & Parameters

  1. GCD(b, denom) → firstGCD
  2. Polygon((instructionEdge, y(Corner[1])), (instructionEdge, y(Corner[3])), Corner[4], Corner[1]) → instruction, instructionRight, instructionTop, instructionLeft, instructionBottom
  3. Line((x(Corner[1]) + ((2 * indent) * screenwidth), 0), yAxis) → align1
  4. Line((x(Corner[1]) + ((3 * indent) * screenwidth), 0), yAxis) → align2
  5. Line((x(Corner[1]) + ((4 * indent) * screenwidth), 0), yAxis) → align3
  6. Simplify((a * x^(2)) + (b * x) + c) → f
  7. PrimeFactors(absDiscriminant) → primeFactors
  8. Unique(primeFactors) → uniqueFactors
  9. Length(uniqueFactors) → numberFactors
  10. Sequence(CountIf[x ≟ Element[uniqueFactors, i], primeFactors], i, 1, numberFactors) → factorRepetitions
  11. Product(Sequence[Element[uniqueFactors, i]^(floor(Element[factorRepetitions, i] / 2)), i, 1, numberFactors]) → outsideroot
  12. If(discriminant < 0, "i", "") → imaginary_1
  13. GCD(outsideroot, denom) → secondGCD
  14. Textfield(a) → inputBox1
  15. Textfield(b) → inputBox2
  16. Textfield(c) → inputBox3
  17. ComplexRoot(f) → z_1, z_2
  18. If(discriminant < 0, "no", If[discriminant > 0, "two", "one"]) → intercepts
  19. If(discriminant < 0, "no real solutions and two imaginary solutions", If[discriminant > 0, "two real solutions and no imaginary solutions", "one real solution and no imaginary solutions"]) → solutions
  20. Simplify((a * x^(2)) + c) → leftside
  21. Simplify(((-b) * x)) → rightside

AI Drawing Prompt Reference

Draw the graph of a quadratic function and show its relationship with the solutions of the equation 2x^2 + 9 = –8x. First, plot the function and mark its x-intercepts as the real solutions of the equation. Then, calculate the discriminant; if it's negative, represent the imaginary solutions (e.g., with dashed lines or special symbols). Finally, display the coefficients and discriminant values in text boxes, distinguishing real and imaginary solutions with different colors.
The prompt above was compiled from the original drawing commands and is for reference only.