MathPlotAI Logo MathPlotAI

Completing the Square

Completing the Square
Loading the math board and drawing, please wait…
2018-06-23 16:04
FunctionCoordinate GeometryGeometric Construction
This example demonstrates how to convert a quadratic polynomial into vertex form using the method of completing the square. Key mathematical concepts include quadratic polynomials, completing the square, and vertex form. It utilizes commands such as If, Segment, Point, Vector, Midpoint, Intersect, Polygon, Translate, Rotate, and Textfield in GeoGebra. Suitable for middle school and above students to learn about the graph and properties of quadratic functions.

GeoGebra Commands & Parameters

  1. If(c_1 ≥ 1 ∧ c_1 ≤ 7.5, c_1 - 1, If[c_1 < 1, 0, 6.4]) → bb
  2. If(bb > 2 ∧ bb ≤ 3, bb - 2, If[bb ≤ 2, 0, 1]) → d3
  3. Segment(A, B) → f
  4. Point(Circle[D, f]) → E
  5. Vector(H, E) → u
  6. If(bb > 1 ∧ bb ≤ 2, bb - 1, If[bb ≤ 1, 0, 1]) → d2
  7. Point(Circle[H, f]) → I
  8. Midpoint(H, J) → K
  9. Intersect(xAxis, yAxis) → C
  10. Segment(D, E) → g
  11. Polygon(D, E, 4) → poly1, h, i, j, k, F, G
  12. Segment(H, I) → l
  13. Polygon(H, J, JJ, I) → q1, h_1, j_1, jj, i_1
  14. Polygon(H, K, KK, I) → q2, h_2, k_1, kk, i_2
  15. Polygon(K, J, JJ, KK) → q3, k_2, j_2, jj_1, kk_1
  16. If(c_1 ≤ 1, c_1, 1) → d1
  17. Vector(K, D) → v
  18. Translate(K, Vector[(d3 * u)]) → K'
  19. Translate(KK, Vector[(d3 * u)]) → KK'
  20. Translate(I, Vector[(d3 * u)]) → I'
  21. Translate(H, Vector[(d3 * u)]) → H'
  22. Polygon(H', K', KK', I') → q2', h', k', kk', i'
  23. Rotate(K, (-90° * d2), K) → K'_1
  24. Rotate(J, (-90° * d2), K) → J'
  25. Rotate(JJ, (-90° * d2), K) → JJ'
  26. Rotate(KK, (-90° * d2), K) → KK'_1
  27. Polygon(K'_1, J', JJ', KK'_1) → q3', k'_1, j', jj', kk'_1
  28. Translate(J', Vector[(v * d3)]) → J''
  29. Translate(JJ', Vector[(v * d3)]) → JJ''
  30. If(bb ≤ 1, bb, 1) → c2
  31. Translate(KK'_1, Vector[(v * d3)]) → M
  32. Translate(K'_1, Vector[(v * d3)]) → N
  33. Translate(J', Vector[(v * d3)]) → J''_1
  34. Translate(JJ', Vector[(v * d3)]) → JJ''_1
  35. Translate(KK'_1, Vector[(v * d3)]) → O
  36. Polygon(N, J''_1, JJ''_1, O) → q3'', n, j''_1, jj''_1, o
  37. Segment(M, M1) → m
  38. If(bb > 3 ∧ bb ≤ 4, bb - 3, If[bb ≤ 3, 0, 1]) → d4
  39. If(bb > 4 ∧ bb ≤ 5, bb - 4, If[bb ≤ 4, 0, 1]) → d5
  40. Segment(JJ''_1, L) → p
  41. Segment(V, P) → q
  42. Vector(Q, S) → w
  43. Vector(T, U) → d
  44. Translate(W, Vector[(w * d1)]) → W'
  45. Translate(Z, Vector[(d * d1)]) → Z'
  46. Midpoint(h') → B_1
  47. Midpoint(n) → A_1
  48. Midpoint(p) → C_1
  49. Midpoint(q) → D_1
  50. Midpoint(kk') → E_1
  51. Polygon(JJ''_1, L, 4) → poly2, r, s, t, e, F_1, G_1
  52. Midpoint(L, E) → H_1
  53. Vector(I_1, J_1) → u_1
  54. Vector(J_1, I_1) → v_1
  55. Vector(K_1, L_1) → w_1
  56. Vector(L_1, K_1) → a_1
  57. Textfield(b) → InputBox1
  58. Textfield(cc) → InputBox2
  59. Corner(text17, 2) → M_1
  60. Corner(text18, 2) → M_2
  61. Corner(text19, 2) → M_3
  62. Corner(text1, 2) → M_4

AI Drawing Prompt Reference

Draw a quadratic function in vertex form, including points A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, and segments, vectors, and polygons. First, draw segment AB, then take point E on the circle with center D and radius AB. Next, draw vector HE and find its midpoint K. Then, draw the intersection point C of the x-axis and y-axis, and polygon DEFGHIJK. Through rotation and translation, construct new polygons and points to form the complete figure.
The prompt above was compiled from the original drawing commands and is for reference only.