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H2M 2019 Q2-2

H2M 2019 Q2-2
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2020-06-17 15:46
FunctionProbability & StatisticsInequality
This example demonstrates the solution process of the second question in the second part of H2M 2019. The core mathematical concepts involved include function graphs, inequalities, and conditional probability. Using GeoGebra commands such as Random, Solutions, and Element, the solution steps are dynamically displayed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Random(1, 10) → a
  2. Random(1, 10) → b
  3. Random(1, 10) → c
  4. Random(1, 10) → d
  5. Solutions(f1(x) > 0) → l1
  6. Solutions(f2(x) > 0) → l2
  7. Element(l2, 1) → i
  8. Element(l2, Length[l2]) → j
  9. Element(l1, 1) → e
  10. Element(l1, 2) → h
  11. Asymptote(f2) → l3
  12. Element(l3, 1) → k
  13. Element(l3, 1) → l
  14. Element(l3, 3) → m
  15. Solutions(f1 = 0) → l4

AI Drawing Prompt Reference

Draw the graphs of two functions f1(x) and f2(x), where the solution set of f1(x) > 0 is shown with a dashed line and the solution set of f2(x) > 0 is shown with a solid line. Randomly generate parameters a, b, c, and d, with f1(x) = ax^2 + bx + c and f2(x) = dx^2 + bx + c. Display the asymptote of f2(x) with a dashed line.
The prompt above was compiled from the original drawing commands and is for reference only.