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Writing Square Root Functions from Graphs

Writing Square Root Functions from Graphs
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2023-05-03 00:33
FunctionGeometric ConstructionGraphing
In collections Square Root Function Anatomy: Exploration
This example demonstrates how to derive the square root function from geometric graphs. Key mathematical concepts include function graphs, roots, and square operations. Construction involves GeoGebra commands such as Point, Line, Vector, and others. Suitable for middle or high school mathematics to understand the relationship between functions and geometry.

GeoGebra Commands & Parameters

  1. Point(Segment[(h + 1, y(C) + 10), (h + 1, y(C) - 10)]) → D
  2. Line(A, B) → f
  3. Vector(A, C) → u
  4. Polygon(A, C, B) → t1, b, a_1, c
  5. Segment(A, C) → h_{1}
  6. Vector(C, D) → v
  7. Vector((h, 0), A) → w
  8. Vector((0, 0), (h, 0)) → j
  9. RandomElement({-8, -7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7, 8}) → n
  10. Random(-8, 8) → o
  11. Random(-8, 8) → p
  12. If(h ≟ o, "Horizontal shift is correct!", "Horizontal shift is not correct.") → text9
  13. If(n ≟ rise, "Vertical stretch is correct!", "Vertical stretch is not correct.") → text10
  14. If(p ≟ y(A), "Vertical shift is correct!", "Vertical shift is not correct.") → text11
  15. Textfield(s) → InputBox1

AI Drawing Prompt Reference

Draw a coordinate plane with a line and a right triangle formed by three points, with the right angle vertex on the horizontal axis. From this vertex, draw a horizontal vector to the right, a vertical vector upward, and a slanted vector for the hypotenuse. Above the vertex, draw a vertical dashed line and place a point on it, then draw a vector from that point to the triangle's top vertex. Also, on the horizontal axis, mark a vector from the origin to a point, and another vector from that point to the right-angle vertex. Next to the figure, add three input boxes for horizontal shift, vertical stretch, and vertical shift, along with text showing whether each value is correct.
The prompt above was compiled from the original drawing commands and is for reference only.