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Zeroes of Quadratic Polynomial

Zeroes of Quadratic Polynomial
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2018-02-17 23:08
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the zeroes of a quadratic polynomial and their geometric significance. It involves core math concepts like quadratic functions, zeroes, factoring, and analytical geometry. GeoGebra commands and objects such as TableText, Textfield, Root, and Factor are used in the construction. Suitable for high school mathematics teaching and function graph analysis.

GeoGebra Commands & Parameters

  1. TableText({{A1, B1, C1}, {A2, B2, C2}, {A3, B3, C3}, {A4, B4, C4}, {A5, B5, C5}, {A6, B6, C6}, {A7, B7, C7}, {A8, B8, C8}, {A9, B9, C9}, {A10, B10, C10}, {A11, B11, C11}}, "|_") → text1
  2. Textfield(f) → inputBox1
  3. Root(f) → A, B, C, D, E
  4. TableText({{A1, B1, C1}, {A2, B2, C2}, {A3, B3, C3}, {A4, B4, C4}, {A5, B5, C5}, {A6, B6, C6}, {A7, B7, C7}, {A8, B8, C8}, {A9, B9, C9}, {A10, B10, C10}, {A11, B11, C11}, {A12, B12, C12}, {A13, B13, C13}, {A14, B14, C14}, {A15, B15, C15}, {A16, B16, C16}, {A17, B17, C17}, {A18, B18, C18}, {A19, B19, C19}, {A20, B20, C20}, {A21, B21, C21}, {A22, B22, C22}}, "|_") → text3
  5. Factor(f) → g
  6. TableText({{A1, B1, C1}, {A2, B2, C2}, {A3, B3, C3}, {A4, B4, C4}, {A5, B5, C5}, {A6, B6, C6}, {A7, B7, C7}, {A8, B8, C8}, {A9, B9, C9}, {A10, B10, C10}, {A11, B11, C11}, {A12, B12, C12}, {A13, B13, C13}, {A14, B14, C14}, {A15, B15, C15}, {A16, B16, C16}, {A17, B17, C17}, {A18, B18, C18}, {A19, B19, C19}, {A20, B20, C20}, {A21, B21, C21}, {A22, B22, C22}}, "|_") → text2

AI Drawing Prompt Reference

Draw the graph of a quadratic function, showing its zeroes, factored form, and geometric significance. First, input a quadratic function expression, then calculate and mark the zeroes of the function. Next, display the factored form of the function. Finally, use tables to list the zeroes and the factored results separately to observe their relationship.
The prompt above was compiled from the original drawing commands and is for reference only.