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

-

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

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

f\,(x)\; =

Hilfe:

Kann man dem Graphen
den Wert von a ansehen?

Gewiss: 
Man liest einfach den Funk-
tionswert bei x=1 ab.

Aufgabe 1
Experiemtiere mit den Schiebereglern.
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.

a = 1 (slider from -5 to 5, step 0.1)
f(x) = a * x^(2.0)
g(x) = x^(2.0)
Text3: abs(a) + ""
Text4: abs(a) + ""
Text9: a + ""
P: (1.0, f(1.0))
u = Vector(P, (0.0, y(P)))
P0: (0.0, y(P))
Text6: y(P) + ""
b = false
Text12: a + ""
c = Segment((1.0, 0.0), P)
Vieleck1, d, e, h, i = Polygon((-4.1, -2.65), (7.2, -2.65), (7.2, -4.93), (-4.1, -4.93))
j = false
p_1(x) = 0.5 * x^(2.0)
p_2(x) = -2.0 * x^(2.0)
p_3(x) = -(0.2) * x^(2.0)
A: (1.0, p_1(1.0))
B: (1.0, p_2(1.0))
C: (1.0, p_3(1.0))
v_2 = Vector((1.0, p_2(1.0)), (0.0, p_2(1.0)))
v_1 = Vector((1.0, p_1(1.0)), (0.0, p_1(1.0)))
v_3 = Vector((1.0, p_3(1.0)), (0.0, p_3(1.0)))
D: (0.0, p_1(1.0))
E: (0.0, p_2(1.0))
F: (0.0, p_3(1.0))
k = Segment((1.0, p_1(1.0)), (1.0, p_2(1.0)))

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)