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Quadratic Graphs and Line of Symmetry

Quadratic Graphs and Line of Symmetry
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2013-11-15 10:14
FunctionCoordinate GeometryOptimization
This example demonstrates the plotting of quadratic function graphs and the determination of their line of symmetry. Key math concepts include quadratic functions, vertex, axis of symmetry, and extreme points. Construction highlights involve using GeoGebra commands like Textfield, Extremum, Intersect, Line, Point, and objects such as sliders and points to input coefficients a, b, c, calculate the vertex, and draw the axis of symmetry. Suitable for high school mathematics education to understand the characteristics of quadratic function graphs and symmetry.

GeoGebra Commands & Parameters

  1. Textfield(a) → inputBox1
  2. Textfield(b) → inputBox2
  3. Textfield(c) → inputBox3
  4. Extremum(a * x^(2) + b * x + c) → A
  5. Intersect(d, xAxis, 1) → B
  6. Intersect(d, xAxis, 2) → C
  7. Intersect(d, yAxis, 1) → D
  8. Line(A, yAxis) → e
  9. Intersect(e, xAxis) → E
  10. Point(d) → F

AI Drawing Prompt Reference

Draw a quadratic function graph by inputting coefficients a, b, and c, find the vertex A, the intersection points B and C with the x-axis, and the intersection point D with the y-axis. Draw the y-axis as the axis of symmetry e, find the intersection point E of the axis of symmetry with the x-axis, and mark the vertex A and the intersection point D on the graph.
The prompt above was compiled from the original drawing commands and is for reference only.