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AM 2019 P2 Q10

AM 2019 P2 Q10
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2020-06-13 19:31
FunctionParametric EquationGeometric Construction
This example demonstrates the solution process for question 10 in the 2nd paper of the 2019 AM. It involves quadratic functions, quadrilaterals, and parametric curves. Through button operations, it dynamically displays the quadratic function graph, quadrilateral changes, and parametric curves. Suitable for high school mathematics teaching and learning.

GeoGebra Commands & Parameters

  1. Random(3, 7) → c
  2. Random(-2, -5) → b
  3. Random(1, 1) → a
  4. Simplify(((-b) * α) - c) → f
  5. Simplify(((-b) * f(α)) - (c * α)) → g
  6. Polynomial((a * x^(2)) + (b * x) + c) → h
  7. Coefficients(g) → l1
  8. Coefficients(p) → l2

AI Drawing Prompt Reference

Draw a quadratic function graph with coefficients generated by three random numbers. Construct a parallelogram with its vertex at the origin and dynamically change its shape by adjusting parameters. Finally, draw a parametric curve whose equation is derived from the quadratic function.
The prompt above was compiled from the original drawing commands and is for reference only.