Imaginary Parabola

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2019-11-29 01:41

This example demonstrates the graph of an imaginary parabola. It involves complex numbers and quadratic equations. Using GeoGebra commands such as Point, Segment, Circle, etc., the imaginary parabola can be constructed. Suitable for high school mathematics education and learning about quadratic equations and complex numbers.

GeoGebra Commands & Parameters

Point(f) → A
Point(f) → B
Point(f) → C
Point(f) → D
Point(f) → E
Point(f) → F
Segment(E, F) → g
Segment(C, D) → h
Segment(A, B) → i_2
Point(f) → G
Point(f) → H
Segment(G, H) → j
Point(f) → I
Point(f) → J
Segment(J, I) → k
Point(f) → K
Point(f) → L
Point(f) → M
Point(f) → N
Segment(K, M) → l
Segment(L, N) → m
Point(Circle[O, 2^(0.5)]) → P
Segment(O, P) → n
Point(Circle[O, 5^(0.5)]) → Q
Segment(O, Q) → p
Point(Circle[O, 1]) → S
Segment(O, S) → q
Point(Circle[P, 1]) → T
Segment(P, T) → r
Point(Circle[Q, 2]) → U
Segment(Q, U) → s
Point(Circle[O, 1]) → V
Segment(V, O) → t
Circle(O, 1) → c
Segment(P, D) → a
Segment(Q, L) → b
Integral(f(x) + (-5^(0.5)) - 2^(0.5)) → f_1
Mirror(O, eq1) → O'
Mirror(P, eq1) → P'
Segment(O', P') → n'
Mirror(O, eq1) → O'_1
Mirror(Q, eq1) → Q'
Segment(O'_1, Q') → p'
Mirror(V, eq1) → V'
Mirror(O, eq1) → O'_2
Segment(V', O'_2) → t'
Mirror(Q, eq1) → Q'_1
Mirror(U, eq1) → U'
Segment(Q'_1, U') → s'
Mirror(P, eq1) → P'_1
Mirror(T, eq1) → T'
Segment(P'_1, T') → r'
Mirror(O, eq1) → O'_3
Mirror(S, eq1) → S'
Segment(O'_3, S') → q'
Mirror(P, eq1) → P'_2
Mirror(D, eq1) → D'
Segment(P'_2, D') → a'
Mirror(Q, eq1) → Q'_2
Mirror(L, eq1) → L'
Segment(Q'_2, L') → b'
Segment(O, C_1) → i
Segment(C_1, z_4) → e
Segment(z_1, z_3) → g_1
Segment(O', C_1) → h_1