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

-

+

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

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

Aufgabe 2

Ermittle\; die\; zu\; den\; Parabeln\; p_1,\; p_2\; und\; p_3\; gehörenden\; Funktionsgleichungen.

d = 0 (slider from -5 to 5, step 0.1)
f(x) = (x - d)^(2.0)
g(x) = x^(2.0)
Text3: abs(d) + ""
v2 = Vector((2.0, g(2.0)), (2.0 + d, f(2.0 + d)))
v1 = Vector((1.0, g(1.0)), (1.0 + d, f(1.0 + d)))
vw2 = Vector((sqrt(2.0), g(sqrt(2.0))), (sqrt(2.0) + d, f(sqrt(2.0) + d)))
vw3 = Vector((sqrt(3.0), g(sqrt(3.0))), (sqrt(3.0) + d, f(sqrt(3.0) + d)))
vw5 = Vector((sqrt(5.0), g(sqrt(5.0))), (sqrt(5.0) + d, f(sqrt(5.0) + d)))
v0 = Vector((0.0, 0.0), (d, f(d)))
P = Midpoint((1.0, g(1.0)), (1.0 + d, f(1.0 + d)))
Text6: d + ""
vm05 = Vector((-sqrt(0.5), g(-sqrt(0.5))), (-sqrt(0.5) + d, f(-sqrt(0.5) + d)))
vmw15 = Vector((-sqrt(1.5), g(-sqrt(1.5))), (-sqrt(1.5) + d, f(-sqrt(1.5) + d)))
vmw25 = Vector((-sqrt(2.5), g(-sqrt(2.5))), (-sqrt(2.5) + d, f(-sqrt(2.5) + d)))
vmw35 = Vector((-sqrt(3.5), g(-sqrt(3.5))), (-sqrt(3.5) + d, f(-sqrt(3.5) + d)))
vmw55 = Vector((-sqrt(5.5), g(-sqrt(5.5))), (-sqrt(5.5) + d, f(-sqrt(5.5) + d)))
vmw45 = Vector((-sqrt(4.5), g(-sqrt(4.5))), (-sqrt(4.5) + d, f(-sqrt(4.5) + d)))
Vieleck1, a, b, c, e = Polygon((-4.14, -0.63), (7.16, -0.63), (7.16, -2.91), (-4.14, -2.91))
h = false
p_1(x) = (x + 2.9)^(2.0)
p_2(x) = (x + 0.9)^(2.0)
p_3(x) = (x - 3.2)^(2.0)
g1(x) = x^(2.0)

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)