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Graphing Quadratic Functions by GreenMaths

Graphing Quadratic Functions by GreenMaths
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2015-01-29 20:13
FunctionCoordinate GeometryGraphing
In collections Patterns & Equations
This example demonstrates how to graph any quadratic function. It allows finding the corresponding y value for a given x value and vice versa. The axis of symmetry is also identified. Commands used include Point, Intersect, OrthogonalLine, Segment, Midpoint, Sum, etc. Suitable for students learning about quadratic functions from middle school onwards.

GeoGebra Commands & Parameters

  1. Point(yAxis) → R
  2. Point(f) → A
  3. Intersect(f, yAxis, 1) → B
  4. Point(f) → C
  5. Point(f) → D
  6. Point(f) → E
  7. Point(f) → F
  8. Point(f) → G
  9. Point(f) → H
  10. Point(f) → I
  11. Point(f) → J
  12. Point(f) → K
  13. Point(f) → L
  14. OrthogonalLine(R, yAxis) → l
  15. Intersect(f, l, 1) → S
  16. OrthogonalLine(S, xAxis) → m
  17. Intersect(m, xAxis) → U
  18. Segment(S, U) → p
  19. Point(xAxis) → M
  20. OrthogonalLine(M, xAxis) → g
  21. Intersect(f, g, 1) → N
  22. OrthogonalLine(N, yAxis) → h
  23. Intersect(h, yAxis) → O
  24. Segment(M, N) → i
  25. Segment(N, O) → j
  26. Midpoint(F, G) → P
  27. Point(f) → W
  28. Point(f) → Z
  29. Point(f) → A_1
  30. Point(f) → B_1
  31. Point(f) → C_1
  32. Point(f) → D_1
  33. Intersect(p_1, xAxis, 1) → F_1
  34. OrthogonalLine(F_1, xAxis) → r
  35. Intersect(f, r, 1) → G_1
  36. Intersect(f, l, 2) → H_1
  37. OrthogonalLine(H_1, xAxis) → t
  38. Intersect(t, xAxis) → I_1
  39. Segment(R, H_1) → a_1
  40. Segment(H_1, I_1) → b_1
  41. Segment(R, S) → d
  42. Sum(B2:D2) → E2
  43. Sum(B3:D3) → E3
  44. Sum(B4:D4) → E4
  45. Sum(B5:D5) → E5
  46. Sum(B6:D6) → E6
  47. Sum(B7:D7) → E7
  48. Sum(B8:D8) → E8
  49. Sum(B9:D9) → E9
  50. Sum(B10:D10) → E10
  51. Sum(B11:D11) → E11
  52. Sum(B12:D12) → E12

AI Drawing Prompt Reference

Draw a quadratic function graph and find the corresponding y-value for a given x-value and vice versa, and identify the axis of symmetry. Start by creating a point R on the y-axis, then create a point A on the quadratic function. Find the intersection of the quadratic function with the y-axis at point B, and create several points C to L on the quadratic function. Draw a perpendicular line l from R to the y-axis, find the intersection S of the quadratic function and l, then draw a perpendicular line m from S to the x-axis, find the intersection U of m and the x-axis, and connect S and U. Next, create a point M on the x-axis, draw a perpendicular line g from M to the x-axis, find the intersection N of the quadratic function and g, then draw a perpendicular line h from N to the y-axis, find the intersection O of h and the y-axis, and connect M and N, then connect N and O. Find the midpoint P of F and G, create several points W to Z on the quadratic function, find the intersection F_1 of p and the x-axis, draw a perpendicular line r from F_1 to the x-axis, find the intersection G_1 of the quadratic function and r, find the intersection H_1 of the quadratic function and l, draw a perpendicular line t from H_1 to the x-axis, find the intersection I_1 of t and the x-axis, and connect R and H_1, then connect H_1 and I_1, and connect R and S.
The prompt above was compiled from the original drawing commands and is for reference only.