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Reciprocal Quadratic Functions

Reciprocal Quadratic Functions
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2019-06-02 02:07
FunctionTransformationGraphing
This example demonstrates reciprocal quadratic functions. Key mathematical concepts include reciprocal and quadratic functions. It uses GeoGebra objects such as function graphs and transformations. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Numeric a(-1)
  2. Numeric b(4)
  3. Numeric c(-2)
  4. f(x) = (a * x^(2)) + (b * x) + c
  5. g(x) = 1 / f(x)
  6. ((-b) + sqrt(b^(2) - ((4 * a) * c))) / ((2 * a))
  7. ((-b) - sqrt(b^(2) - (4 * (a * c)))) / ((2 * a))
  8. x = R_{1}
  9. x = R_{2}
  10. y = 0
  11. (R_{1}, 0)
  12. (R_{2}, 0)
  13. ((-b) + sqrt(b^(2) - (4 * (a * (c + 1))))) / ((2 * a))
  14. ((-b) - sqrt(b^(2) - (4 * (a * (c - 1))))) / ((2 * a))
  15. ((-b) + sqrt(b^(2) - (4 * (a * (c - 1))))) / ((2 * a))
  16. ((-b) - sqrt(b^(2) - (4 * (a * (c + 1))))) / ((2 * a))
  17. (I_{1}, -1)
  18. (I_{2}, 1)
  19. (I_{3}, 1)
  20. (I_{4}, -1)

AI Drawing Prompt Reference

Draw a parabola and its reciprocal function, highlighting key points and the axis of symmetry. First, plot the base parabola, then calculate and mark its vertex. Next, graph the reciprocal function, marking its x-intercepts. Finally, label specific points on the reciprocal graph to show transformation characteristics.
The prompt above was compiled from the original drawing commands and is for reference only.