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Quadratic Function Graph Analysis Example

Quadratic Function Graph Analysis Example
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2013-05-17 19:02
FunctionCoordinate GeometryOptimizationGraphing
This example demonstrates how to graph and analyze the quadratic function h(x) = 2x^2 – 11x + 5 using GeoGebra. Key math concepts include properties of quadratic functions, direction of opening, vertex, axis of symmetry, etc. Construction highlights involve commands like If, Factor, Segment, Element, TableText to calculate roots, coefficients, vertex coordinates, and draw geometric elements such as the axis of symmetry and vertex. Suitable for high school mathematics teaching to understand the geometric features of quadratic function graphs.

GeoGebra Commands & Parameters

  1. If(abs(c2) ≟ 1, If[c2 ≟ 1, "", "-"], LaTeX[c2]) → c1
  2. Factor(h) → facth
  3. Factors(h) → factorsh
  4. Segment(A, Ar) → e
  5. Element(factorsh, 1, 1) → factor1
  6. Element(factorsh, 2, 1) → factor2
  7. TableText({{form1, ftext1}, {form2, ftext2}, {form3, ftext3}}) → table1
  8. TableText({{form4, ftext4}, {form5, ftext5}, {form6, ftext6}}) → text6
  9. TableText({{form7, ftext7}, {form8, ftext8}, {form9, ftext9}}) → text8

AI Drawing Prompt Reference

Graph the quadratic function h(x) = 2x^2 – 11x + 5, highlighting the vertex and axis of symmetry. Calculate and display the coefficients, factored form, and roots. Use distinct colors for the function graph and geometric elements, plotting the graph first, then marking the vertex and axis, and finally showing the calculations.
The prompt above was compiled from the original drawing commands and is for reference only.