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Forms of Quadratic Functions

Forms of Quadratic Functions
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2018-11-12 11:05
FunctionCalculusDerivativeParametric EquationGraphing
This example demonstrates the vertex form, standard form, and factored form of quadratic functions, including their graphs and transformations. Key math concepts involve quadratic functions, vertex, axis of symmetry, derivatives, and roots. GeoGebra commands like If, Random, Point, Textfield, Derivative, Root, Vector, Polygon are used in construction. Suitable for high school mathematics teaching and learning function graph transformations.

GeoGebra Commands & Parameters

  1. If(d, ((-b)) / ((2 * a)), If[e, (r + s) / 2, If[f, h]]) → xvertex
  2. If(d, standardform(xvertex), If[e, factoredform(xvertex), If[f, vertexform(xvertex)]]) → yvertex
  3. Random(-10, 10) → yintgoal
  4. Random(-10, 10) → root1goal
  5. Random(-10, 10) → root2goal
  6. Random(1, 3) → dice
  7. Random(-10, 10) → xvertgoal
  8. Random(-10, 10) → yvertgoal
  9. Point({xvertgoal, yvertgoal}) → vertexgoal
  10. If(d, standardform, If[e, factoredform, vertexform]) → chosen
  11. If(dice ≟ 1, chosen(root1goal) ≟ 0 ∧ chosen(root2goal) ≟ 0, If[dice ≟ 2, xvertex ≟ root1goal ∧ yvertex ≟ 0, (yvertex * a) > 0]) → gotx
  12. Textfield(a) → InputBox1
  13. Derivative(test) → dtest
  14. Root(test) → testroots_1, testroots_2
  15. Vector((root1goal + 2.4 - (1.2 / 5 * (root1goal + 10)), -1), B) → v
  16. Vector((root1goal / 2 + root2goal / 2 - 1 - (2.7 / 9.5 * (root1goal / 2 + root2goal / 2)), -1.9), If[x(C) < x(B), C, B]) → w
  17. Vector((root1goal / 2 + root2goal / 2 + 1 - (2.7 / 9.5 * (root1goal / 2 + root2goal / 2)), -1.9), If[x(C) < x(B), B, C]) → g
  18. Vector((xvertgoal + 1.2 - (3 / 20 * (xvertgoal + 10)), yvertgoal - 0.9 + If[yvertgoal ≟ -10, 1.8, 0]), vertexgoal) → i
  19. Vector((root1cust + 2.4 - (1.2 / 5 * (root1cust + 10)), -1), E) → v_1
  20. Vector((root1cust / 2 + root2cust / 2 - 1 - (2.7 / 9.5 * (root1cust / 2 + root2cust / 2)), -1.9), If[x(E) < x(F), E, F]) → w_1
  21. Vector((root1cust / 2 + root2cust / 2 + 1 - (2.7 / 9.5 * (root1cust / 2 + root2cust / 2)), -1.9), If[x(E) < x(F), F, E]) → g_1
  22. Vector((1, y(D)), D + (0.1, 0)) → u_1
  23. Vector((xvertcust + 1.2 - (3 / 20 * (xvertcust + 10)), yvertcust - 0.9 + If[yvertcust ≟ -10, 1.8, 0]), vertcust) → i_1
  24. Textfield(b) → InputBox2
  25. Textfield(c) → InputBox3
  26. Textfield(r) → InputBox4
  27. Textfield(s) → InputBox5
  28. Textfield(h) → InputBox6
  29. Textfield(k) → InputBox7
  30. Root(chosen) → G, H
  31. Polygon(J, K, L, M) → q1, j_1, k_1, l_1, m_1

AI Drawing Prompt Reference

Create an interactive educational graph illustrating three forms of quadratic functions: vertex form, standard form, and factored form. The graph shows a parabola with its vertex, axis of symmetry, and x-intercepts clearly marked. Multiple input boxes allow adjusting coefficients, vertex coordinates, and roots. The derivative curve is displayed, with vectors and arrows indicating the vertex, roots, and axis. A coordinate grid is in the background, with randomly generated target vertex and roots for practice. The layout includes the function plot, input areas, and auxiliary lines, suitable for high school function transformation lessons.
The prompt above was compiled from the original drawing commands and is for reference only.