Interactive Geometry Demo on Symmetry and Hypothesis Testing

GeoGebra Commands & Parameters

1. LaTeX("\text{\mathit{x}}") → text9_1
2. LaTeX("\text{\mathit{y}}") → text9_2
3. Polygon(A, B, C, D, E, F) → poly1, a_1, b_1, c_1, d, e, f
4. Point(d) → G
5. Polygon(G, H, I, D) → poly2, g, h, i, d_1
6. Point(e) → J
7. Point(g) → K
8. Polygon(F, J, K, H) → poly3, f_1, j, k, h_1
9. Segment(L, M) → l
10. Segment(M, N) → m
11. Segment(N, O) → n
12. Segment(O, L) → p
13. Polygon(R, S, T, U) → poly4, r, s, t, u
14. Intersect(xAxis, yAxis) → V
15. Point(xAxis) → W
16. Vector(V, W) → v
17. Point(yAxis) → Z
18. Vector(V, Z) → w
19. Point(yAxis) → A_1
20. Vector(V, A_1) → q
21. Point(xAxis) → B_1
22. Vector(V, B_1) → u_1
23. Point(yAxis) → N_1
24. Polygon(M_1, N_1, O_1) → poly6, o_1, m_2, n_1
25. Polygon(P_1, Q_1, R_1) → poly7, r_1, p_1, q_1
26. Polygon(S_1, T_1, U_1) → poly8, u_2, s_1, t_1
27. Segment(V_1, W_1) → e_1
28. Segment(Z_1, A_2) → f_2
29. Segment(B_2, C_2) → g_2
30. Segment(D_2, E_2) → h_2
31. Segment(F_2, E_2) → n_2
32. LaTeX("\text{Click the button to solve the problem.}") → text3
33. LaTeX("\text{\mathbf{Note}\mathbf{:} Use the (Data Kit) \\to return to the original \\problem or randomly generate \\a similar practice problem.\\Use the (Definition) to \\review words to know.}") → text4
34. LaTeX("\text{Recall what we know.}") → text2
35. LaTeX("\text{Check for symmetry across the origin.}") → text6
36. LaTeX("\text{Check for symmetry across the \textcolor{#000099}{\mathit{y}}-axis.}") → text2_7
37. LaTeX("\text{The function is even.}") → text2_9
38. LaTeX("\text{We can see that this graph is symmetric across the \textcolor{#000099}{\mathit{y}}-axis.\\We can also see that the function is an upside-down parabola that is\\shifted up \textcolor{#000099}{2} units.To verify that this function is even,find the equation\\of the graph,\textcolor{#000099}{\mathit{f(x)} = –\mathit{x}^2 + 2},and see if it is equal to \textcolor{#000099}{\mathit{f(–x)}}.}") → text2_5
39. LaTeX("\text{We can see that this graph is not symmetric across the origin.}") → text2_3
40. LaTeX((("\text{Function:\textcolor{#000099}{\mathit{f(x)} = -\mathit{x}^2+{" * a) * "}}}")) → text2_2
41. Polygon(C_1, D_1, E_1, F_1) → q1, c_2, d_2, e_2, f_3
42. LaTeX("\text{\mathbf{Function:}\;A relation or expression involving one or more variables.}") → text2_{16}
43. LaTeX("\text{\mathbf{Symmetric:}\;Made up of exactly similar parts facing each other or around an axis.}") → text2_{13}
44. LaTeX("\text{Determine whether the following graph is even,odd,or neither.}") → text1_1
45. LaTeX("\text{An odd function is symmetric across the origin,and an even function\\is symmetric across the \textcolor{#000099}{\mathit{y}}-axis.}") → text2_1
46. Polygon(G_1, H_1, G_2) → t1, g_1, g_3, h_3
47. LaTeX("\text{0}") → text5
48. LaTeX("\text{-}") → text7
49. LaTeX((("\text{\textcolor{#000099}{\mathit{f(–x)} = –(–\mathit{x})^2 + 2 = –\mathit{x}^2 + {" * a) * "}}}")) → text2_8
50. LaTeX((("\text{Step {" * Slider) * "} of 8}")) → text2_{10}
51. LaTeX("\text{However,we can verify this by taking a point on the graph and\\reflecting it.Let’s use the point \textcolor{#000099}{(1,1)}.First,reflect it across the\\\textcolor{#000099}{\mathit{x}}-axis to \textcolor{#000099}{(1,–1)}.Then reflect it across the \textcolor{#000099}{\mathit{y}}-axis to \textcolor{#000099}{(–1,–1)}.There\\is no point \textcolor{#000099}{(–1,–1)} on the graph,so this graph is not symmetric\\across the origin.}") → text1