a

Quadratische Funktionen
verschiedene Terme für die gleiche Funktion

a

a

1. Allgemeine Form

2. Scheitelpunktform

3. Faktorisierte Form

d

e

(funktioniert, solange kein Schieberegler
über seine Grenze geht.)

a_1 = 0.8 (slider from -10 to 10, step 0.1)
b = 5.6 (slider from -10 to 10, step 0.1)
c = 5.5 (slider from -10 to 10, step 0.1)
a_2 = 0.8 (slider from -10 to 10, step 0.1)
d = -3.4999999999999996 (slider from -10 to 10, step 0.1)
e = -4.299999999999999 (slider from -10 to 10, step 0.1)
a_3 = 0.8 (slider from -10 to 10, step 0.1)
x_1 = -1.1815953761260745 (slider from -10 to 10, step 0.1)
x_2 = -5.818404623873924 (slider from -10 to 10, step 0.1)
f(x) = (a_1 * x^(2)) + (b * x) + c
f_A: "f(x)=\textcolor{#FF0000}{" + (LaTeX[a_1]) + "}x^2\textcolor{#0000FF}{ " + (LaTeX[If[b < 0, "", "+"]]) + "" + (LaTeX[b]) + " }x\textcolor{pinegreen}{ " + (LaTeX[If[c < 0, "", "+"]]) + "" + (LaTeX[c]) + "}"
f_S: "f(x)=\textcolor{red}{" + (LaTeX[a_2]) + "}(x-\textcolor{#CC9900}{" + (LaTeX[If[d < 0, "(", ""]]) + "" + (LaTeX[d]) + "" + (LaTeX[If[d < 0, ")", ""]]) + "})^2 " + (LaTeX[If[e < 0, "", "+"]]) + "\textcolor{#CC66FF}{ " + (LaTeX[e]) + "}"
f_N: "f(x)=\textcolor{red}{" + (LaTeX[a_3]) + "}(x-" + (LaTeX[If[x_1 < 0, "(", ""]]) + "\textcolor{#993300}{" + (LaTeX[x_1]) + "} " + (LaTeX[If[x_1 < 0, ")", ""]]) + " ) (x-" + (LaTeX[If[x_2 < 0, "(", ""]]) + " \textcolor{#993300}{ " + (LaTeX[x_2]) + "}" + (LaTeX[If[x_2 < 0, ")", ""]]) + " )"
Text3: "Scheitelpunkt \quad S=(\textcolor{#CC9900}{" + (LaTeX[d]) + "}/\textcolor{#CC66FF}{" + (LaTeX[e]) + "})"
Text4: "Nullstellen: x_1=\textcolor{#993300}{" + (LaTeX[x_1]) + "}, x_2=\textcolor{#993300}{" + (LaTeX[x_2]) + "}"
A = (4, 2)
B = (21, 2)
C = (4, 4)
D = (21, 4)
E = (4, 6)
F = (21, 6)
S: (d, e)
s_x = Segment((0, 0), (d, 0))
s_y = Segment((d, 0), (d, e))
N_1: (x_1, 0)
N_2: (x_2, 0)
Disk: (b / ((2 * a_1)))^(2) - c / a_1
w: sqrt(Disk)
a: ((-b)) / ((2 * a_1))
x11: a + w
x22: a - w