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Investigating the Discriminant

Investigating the Discriminant
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2011-10-30 19:58
FunctionCoordinate GeometryGeometric Construction
In collections Quadratic functions
This example demonstrates the intersection points of a quadratic equation [math]ax^2+bx+c[/math] and a linear equation [math]mx+d[/math], by adjusting the coefficients [math]a, b, c, m, d[/math]. Core mathematical concepts include quadratic equations, discriminants, and linear equations. GeoGebra objects used include [math]a, b, c, f, m, d, g, B, C, E, D, F, G, H, I, A, text3, J, K, L, M, text1, text2[/math]. Suitable for secondary school and above students to learn about the discriminant and its geometric meaning.

GeoGebra Commands & Parameters

  1. Numeric a(1.0)
  2. Numeric b(-1.0)
  3. Numeric c(-3.0)
  4. f(x) = a * x^(2) + b * x + c
  5. Numeric m(2.0)
  6. Numeric d(2.0)
  7. g(x) = m * x + d
  8. Point B(6.6, 9.896818810511755)
  9. Point C(6.56, 1.3)
  10. Point E(12.24, 9.896818810511755)
  11. Point D(12.2, 1.3)
  12. Point F(6.94, -3.670816044260028)
  13. Point G(6.94, -9.74896265560166)
  14. Point H(12.44, -9.74896265560166)
  15. Point I(12.44, -3.670816044260028)
  16. (b - m)^(2) - 4 * a * (c - d)
  17. Point J(-10.46, 10.351313969571232)
  18. Point K(-10.46, 8.851313969571232)
  19. Point L(-4.46, 8.851313969571232)
  20. Point M(-4.46, 10.351313969571232)

AI Drawing Prompt Reference

Draw the intersection points of a quadratic function and a linear function by adjusting their coefficients a, b, c, and m, d respectively. Highlight several key points including the intersection points of the two functions and points calculated from the discriminant, and label the value of the discriminant.
The prompt above was compiled from the original drawing commands and is for reference only.