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Linking Quadratic Factorising to Graphical Roots

Linking Quadratic Factorising to Graphical Roots
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2016-06-08 02:39
FunctionCoordinate GeometryOptimization
This example visually demonstrates the relationship between quadratic factorization and roots. Key mathematical concepts include quadratic equations, factorization, and roots. It utilizes commands like Random, If, Textfield, Root, and Extremum in GeoGebra. Suitable for middle school and above students to learn about quadratic equations.

GeoGebra Commands & Parameters

  1. Random(-10, 10) → b
  2. Random(1, 9) → a
  3. Random(1, 9) → c
  4. Random(-10, 10) → d
  5. If((a * d) + (b * c) < 0, (-((a * d) + (b * c))), (a * d) + (b * c)) → B
  6. If((b * d) < 0, ((b * d) * (-1)), (b * d)) → C
  7. If((a * d) + (b * c) < 0, "-", "+") → sign1
  8. If((b * d) < 0, "-", "+") → sign2
  9. If(b < 0, "- ", "+") → sign3
  10. If(d < 0, "- ", "+") → sign4
  11. Textfield(ansA) → InputBox1
  12. Textfield(ansB) → InputBox2
  13. Textfield(ansC) → InputBox3
  14. Textfield(ansD) → InputBox4
  15. Root(f) → L, M
  16. Textfield(root1) → InputBox5
  17. Textfield(root2) → InputBox6
  18. Extremum(f) → N

AI Drawing Prompt Reference

Draw a quadratic function graph with coefficients a, b, c, and d generated by random numbers. Calculate the roots and vertex of the function based on these coefficients. Display the roots and vertex using input boxes. Note that the sign of the roots depends on the signs of b and d, and the sign of the vertex depends on the signs of a and d.
The prompt above was compiled from the original drawing commands and is for reference only.