Schnitt von Gerade und Parabel
Author: Werner Knobloch
Date: 8. März 2010

\scalebox{0.8}  \text {Mit den Reglern kannst du die Funktionsterme der Parabel und der Geraden beeinflussen.}\
 \scalebox{0.8}  \text {Die Schnittstellen werden, sofern sie existieren, auf der x-Achse angezeigt.}

\scalebox{0.9} \text{ Werner Knobloch 2011}

\scalebox{0.9} \text{ Schnitt von Gerade und Parabel}

a = 1.4 (slider from -5 to 5, step 0.1)
b = 2 (slider from -5 to 5, step 0.1)
c = -1.2 (slider from -5 to 5, step 0.1)
m = -0.6 (slider from -5 to 5, step 0.1)
d = 1.4 (slider from -5 to 5, step 0.1)
f(x) = (a * x^(2)) + (b * x) + c
g(x) = (m * x) + d
A, B = Intersect(f, g)
h = Line(A, yAxis)
i = Line(B, yAxis)
C = Intersect(h, xAxis)
D = Intersect(i, xAxis)
u = Vector(A, C)
v = Vector(B, D)
Formeln = true
aVZ = If(a  <  0, "(" + a + ")", "" + a + "")
bVZ = If(b  <  0, "(" + b + ")", "" + b + "")
cVZ = If(c  <  0, "(" + c + ")", "" + c + "")
bminusmVZ = If(b - m  <  0, "(" + (b - m) + ")", "" + (b - m) + "")
cminusdVZ = If(c - d  <  0, "(" + (c - d) + ")", "" + (c - d) + "")
dVZ = If(d  <  0, "(" + d + ")", "" + d + "")
text1: "\scalebox{1.1} {f(x)=a\cdot x^2+b\cdot x+c}\\
\scalebox{1.1} { \; \;  \;  \;  \;  \;  \;      = " + (LaTeX[a]) + "\cdot x^2+ " + (LaTeX[bVZ]) + "\cdot x + " + (LaTeX[cVZ]) + " } "
text2: "\scalebox{1.1} { g(x)=m\cdot x +d }\\
\scalebox{1.1} {\;\;\;\;\;\;\;\;\;= " + (LaTeX[m]) + "\cdot x +" + (LaTeX[dVZ]) + "}"
Text1: "\scalebox{1.0} {Schnittgleichung:}\\
 \scalebox{1.0} { " + (LaTeX[a]) + "x^2+" + (LaTeX[bVZ]) + "x +" + (LaTeX[cVZ]) + " = " + (LaTeX[m]) + "x+" + (LaTeX[dVZ]) + "}\\ 

\scalebox{1.0} {quadratische\; Gleichung:}\\
 \scalebox{1.0} { " + (LaTeX[a]) + " x^2 +" + (LaTeX[bminusmVZ]) + "x +" + (LaTeX[cminusdVZ]) + " = 0}\\\space \\
 \scalebox{1.0} \text {Lösung: }\\
 \scalebox{1.0} {x_1 = \frac{-" + (LaTeX[bminusmVZ]) + "+\sqrt{" + (LaTeX[bminusmVZ]) + "^2 - 4\cdot " + (LaTeX[aVZ]) + " \cdot " + (LaTeX[cminusdVZ]) + "} } {2 \cdot" + (LaTeX[aVZ]) + "} =" + (LaTeX[x(A)]) + "}\\
 \scalebox{1.0} {x_2 = \frac{- " + (LaTeX[bminusmVZ]) + "-\sqrt{" + (LaTeX[bminusmVZ]) + " ^2 - 4\cdot " + (LaTeX[aVZ]) + "  \cdot " + (LaTeX[cminusdVZ]) + " } } {2 \cdot" + (LaTeX[aVZ]) + " } = " + (LaTeX[x(B)]) + "}"