Paper Folding Roots With Parabola

Paper Folding Roots With Parabola
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2018-04-17 09:47
① This example demonstrates how paper-folding operations (reflection via perpendicular bisectors) combined with a parabola can geometrically reveal the roots of a quadratic equation. ② Core mathematical concepts include parabola, roots (zeros), symmetry, perpendicular bisector, midpoint, and intersections of function graphs with axes. ③ Construction highlights: using GeoGebra commands such as LineBisector, Intersect, Circle, Line, Segment, and Midpoint, with objects like parabola p, point A, function f, circle c, line g, etc., the fold lines intersect the parabola to locate the roots. ④ Suitable for upper secondary or introductory university students, this serves as an engaging exploration of the geometric meaning of quadratic roots, and can be used in paper-folding math or dynamic geometry activities.

GeoGebra Commands & Parameters

  1. LineBisector(A, B) → g
  2. Intersect(g, yAxis) → C
  3. Circle(C, A) → d
  4. Line(F, f) → j
  5. Segment(F, D) → k
  6. Midpoint(k) → E

AI Drawing Prompt Reference

Draw a parabola and a perpendicular bisector from a point on the parabola to the y-axis. Use the intersection point as the center to draw a circle passing through the point on the parabola. Connect the point on the parabola to the intersection point on the y-axis with a line, and find the intersection points of this line with the parabola to reveal the roots.
The prompt above was compiled from the original drawing commands and is for reference only.