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2019 AMC P2 Q9: Quadratic Curve and Integral

2019 AMC P2 Q9: Quadratic Curve and Integral
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2020-06-13 14:08
FunctionCoordinate GeometryIntegral
This example demonstrates the quadratic curve and integral problem from the 2019 AMC P2 Q9. Key mathematical concepts include definite integral, symmetry, translation, arithmetic mean, parallelogram, and quadrilaterals. Using GeoGebra commands such as Random, RandomElement, Simplify, Tangent, FractionText, Integral, etc., dynamic geometric figures can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Random(2, 2) → b
  2. RandomElement({3, 4, 6, 7, 8}) → a
  3. Random(1, 2) → d
  4. Simplify(g) → g1
  5. Random(2, 2) → c
  6. Tangent(P, g) → h
  7. FractionText(Slope[h]) → textm
  8. Integral(g, 0, c) → i
  9. SurdText(i, {log(j)}) → textaCurve
  10. RightSide(h) → k
  11. Integral(k1, 0, c) → l
  12. FractionText(y(B)) → textyB
  13. FractionText(l) → textaTrap
  14. Segment((0, 0), (10, 0)) → m
  15. Segment((0, 0), (0, 26)) → n

AI Drawing Prompt Reference

Draw a quadratic curve with a symmetry axis parallel to the x-axis passing through randomly generated points, calculate the definite integral of the curve from 0 to c on the x-axis, and represent the integral area and curve in different colors. Also, plot the tangent line at point P and display its slope and y-intercept, finally adding the x-axis and y-axis to the coordinate system.
The prompt above was compiled from the original drawing commands and is for reference only.