f\,(x)\; =\; x^2

+

-

Aufgabe 2

Ermittle\; die\; zu\; den\; Parabeln 

p_1,\; p_2\; und\; p_3\; gehörenden 

Funktionsgleichungen.

Aufgabe 1
Experimentiere mit dem
Schieberegler.
Erörtere deine Beobachtungen
mit deinem Nachbarn und
notiere im Heft einen Merksatz.

[Kästchen anklicken]

e = 0 (slider from -5 to 5, step 0.1)
f(x) = x^(2.0) + e
g(x) = x^(2.0)
v0 = Vector((0.0, 0.0), (0.0, f(0.0)))
v05 = Vector((0.5, g(0.5)), (0.5, f(0.5)))
vm05 = Vector((-(0.5), g(-(0.5))), (-(0.5), f(-(0.5))))
vm15 = Vector((-(1.5), g(-(1.5))), (-(1.5), f(-(1.5))))
vm25 = Vector((-(2.5), g(-(2.5))), (-(2.5), f(-(2.5))))
v25 = Vector((2.5, g(2.5)), (2.5, f(2.5)))
v15 = Vector((1.5, g(1.5)), (1.5, f(1.5)))
v1 = Vector((1.0, g(1.0)), (1.0, f(1.0)))
v2 = Vector((2.0, g(2.0)), (2.0, f(2.0)))
vm2 = Vector((-(2.0), g(-(2.0))), (-(2.0), f(-(2.0))))
vm1 = Vector((-1.0, g(-1.0)), (-1.0, f(-1.0)))
P = Midpoint((0.0, 0.0), (0.0, f(0.0)))
Text1: e + ""
Text3: abs(e) + ""
P1 = (2.5, -0.5)
P2 = (6.5, -0.5)
P4 = (2.5, -2.3)
P3 = (6.5, -2.3)
b = false
Vieleck1, a, c, d, h = Polygon((2.9, 2.8), (7.0, 2.8), (7.0, -1.5), (2.9, -1.5))
p_1(x) = x^(2.0) + 2.5
p_3(x) = x^(2.0) - 2.3
p_2(x) = x^(2.0) + 1.2

Tool: Eulergerade
Gib 3 Punkte an
Input: A, B, C
Output: Vieleck1, Euler, h_a, h_b, h_c, m_a, m_b, m_c, H, M_a, M_b, M_c, S, U, a, b, c, s_a, s_b, s_c

Vieleck1_1, c_1, a_1, b_1 = Polygon(A, B, C)
Vieleck1, c, a, b = Polygon(A, B, C)
M_a = Midpoint(a)
M_b = Midpoint(b)
M_c = Midpoint(c)
m_a = OrthogonalLine(M_a, a)
m_b = OrthogonalLine(M_b, b)
m_c = OrthogonalLine(M_c, c)
U = Intersect(m_a, m_b)
s_a = Segment(M_a, A)
s_b = Segment(B, M_b)
s_c = Segment(M_c, C)
S = Intersect(s_b, s_a)
h_c = OrthogonalLine(C, c)
h_a = OrthogonalLine(A, a)
h_b = OrthogonalLine(B, b)
H = Intersect(h_a, h_b)
Euler = Line(U, H)

Tool: Feuerbach-Kreis (command Feuerbach)
Gib 3 Punkte an
Input: A, B, C
Output: npc, N, poly1, M_b, M_c, M_a, H, E_1, E_2, E_3, F_1, F_2, F_3, c, a, b

poly1, c, a, b = Polygon(A, B, C)
M_b = Midpoint(b)
M_c = Midpoint(c)
M_a = Midpoint(a)
g = OrthogonalLine(B, b)
h = OrthogonalLine(C, c)
i = OrthogonalLine(A, a)
H = Intersect(i, g)
E_3 = Midpoint(H, C)
E_1 = Midpoint(H, A)
E_2 = Midpoint(H, B)
npc = Circle(M_c, M_a, M_b)
F_2 = Intersect(g, b)
F_3 = Intersect(h, c)
F_1 = Intersect(i, a)
N = Center(npc)