x_0

y_0

Quadratische Funktion - Normalform

Quadratische Funktion - Scheitelpunktform

x_0

y_0

a

x_1

x_2

S( \color{red}{x_0} \color{black} {|} \color{purple} {y_0}\color{black}{)}

\color{red}{x_{1/2}} \color{black} = \frac{- \color{rgb(1,0.4,0)}{b} \color{black} \;\pm\; \sqrt{\color{rgb(1,0.4,0)}{b}\color{black}{^2 - 4}\color{rgb(0,0.6,1)}{a}\color{rgb(0.4,0.6,0)}{c}}}{2\color{rgb(0,0.6,1)}{a}}

abc-Formel

Nullstellen

a = 1 (slider from -5 to 5, step 0.1)
b = 4 (slider from -5 to 5, step 0.1)
c = 4 (slider from -5 to 5, step 0.1)
aKlammer = If(a ≥ 0, LaTeX[a], "(" + (LaTeX[a]) + ")")
bKlammer = If(b ≥ 0, LaTeX[b], "(" + (LaTeX[b]) + ")")
cKlammer = If(c ≥ 0, LaTeX[c], "(" + (LaTeX[c]) + ")")
Text1: "\color{black} f(x) = \color{rgb(0,0.6,1)}\underbrace{" + (LaTeX[aKlammer]) + "}_{a} \color{black}x^2 + \color{rgb(1,0.4,0)}\underbrace{" + (LaTeX[bKlammer]) + "}_{b} \color{black}x + \color{rgb(0.4,0.6,0)}\underbrace{" + (LaTeX[cKlammer]) + "}_{c}"
f(x) = (a * x^(2)) + (b * x) + c
x0: ((-b)) / ((2 * a))
y0: c - b^(2) / ((4 * a))
Text9: "\color{red}x_0 = " + (LaTeX[x0]) + ""
X: (x0 | 0)
Y: (0 | y0)
Text10: "\color{purple} y_0 = " + (LaTeX[y0]) + ""
yPosNF: 50
yPosUmwandlung: yPosNF + 120
xPosUmwandlung: 15
xPosNF: 15
xPosSF: 15
yPosSF: yPosNF + 480
x1 = 1 (slider from -5 to 5, step 0.1)
y1 = -1.6 (slider from -5 to 5, step 0.1)
a1 = 0.6 (slider from -5 to 5, step 0.1)
b1: ((2 * a1) * x1)
c1: (a1 * x1^(2)) + y1^(2)
a1Klammer = If(a1 ≥ 0, LaTeX[a1], "(" + (LaTeX[a1]) + ")")
x1Klammer = If(x1 ≥ 0, LaTeX[x1], "(" + (LaTeX[x1]) + ")")
y1Klammer = If(y1 ≥ 0, LaTeX[y1], "(" + (LaTeX[y1]) + ")")
Text17_{1}: "\color{rgb(0,0.6,1)} a = " + (LaTeX[a]) + " "
Text17: " \color{rgb(1,0.4,0)}b = " + (LaTeX[b1]) + ""
Text18: "\color{rgb(0.4,0.6,0)}c = " + (LaTeX[c1]) + ""
Text20: "\color{rgb(0,0.6,1)} a = " + (LaTeX[a1]) + ""
b1Klammer = If(b1 ≥ 0, LaTeX[b1], "(" + (LaTeX[b1]) + ")")
c1Klammer = If(c1 ≥ 0, LaTeX[c1], "(" + (LaTeX[c1]) + ")")
Nullstellen = Solve(f(x) = 0)
A, B = Intersect(f, xAxis)
S: (x0 | y0)
n1: ((-b) - sqrt(b^(2) - ((4 * a) * c))) / ((2 * a))
gerundetxN1: floor((100 * n1)) ≠ (100 * n1)
n2: ((-b) + sqrt(b^(2) - ((4 * a) * c))) / ((2 * a))
gerundetxN2: floor((100 * n2)) ≠ (100 * n2)
Text8: "f(x) =   \color{rgb(0,0.6,1)}\underbrace{" + (LaTeX[aKlammer]) + " }_{a} \color{black}  \left( x - \color{red} \underbrace{" + (LaTeX[x1Klammer]) + "}_{x_0 = \frac{-b}{2a}}\color{black}\right)^2 +\color{purple}\underbrace{ " + (LaTeX[y1Klammer]) + "}_{y_0 = c - \frac{b^2}{4a}}"
d = false
e = false
xPosFormel: 15
yPosFormel: 170
Text4_{1}: "\color{red}{x_2}\color{black} \; = " + (LaTeX[n2]) + ""
Text3: "\color{red}{x_1} \color{black} \; = " + (LaTeX[n1]) + ""