x_0

y_0

Quadratische Funktion - Normalform

Quadratische Funktion - Scheitelpunktform

Umwandlung

Quadratische Funktion - Scheitelpunktform

x_0

y_0

a

f

Quadratische Funktion - Normalform

Umwandlung

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

a = 0.5 (slider from -5 to 5, step 0.1)
b = -1 (slider from -5 to 5, step 0.1)
c = 2 (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))
Text2: "f(x) = " + (LaTeX[aKlammer]) + " \left( x^2 + \frac{" + (LaTeX[bKlammer]) + "}{" + (LaTeX[aKlammer]) + "}x \right) + " + (LaTeX[cKlammer]) + ""
Text4: "x^2 + \frac{" + (LaTeX[bKlammer]) + "}{" + (LaTeX[aKlammer]) + "}+\left(\frac{" + (LaTeX[bKlammer]) + "}{2\cdot " + (LaTeX[aKlammer]) + "}\right)^2 - \left(\frac{" + (LaTeX[bKlammer]) + " }{2\cdot  " + (LaTeX[aKlammer]) + "}\right)^2"
Text3: "f(x) = " + (LaTeX[aKlammer]) + "\left( " + (LaTeX[Text4]) + "  \right)+  " + (LaTeX[cKlammer]) + ""
Text6: "\left( x - \frac{" + (LaTeX[bKlammer]) + "}{2\cdot " + (LaTeX[aKlammer]) + "}\right)^2 - \left(\frac{" + (LaTeX[bKlammer]) + "}{2\cdot" + (LaTeX[aKlammer]) + "}\right)^2"
Text5: "f(x) = " + (LaTeX[aKlammer]) + "\left( " + (LaTeX[Text6]) + "\right) + " + (LaTeX[cKlammer]) + ""
Text7: "f(x) = " + (LaTeX[aKlammer]) + "\left( x + \frac{" + (LaTeX[bKlammer]) + "}{2 \cdot " + (LaTeX[aKlammer]) + "}\right)^2 -" + (LaTeX[aKlammer]) + " \left( \frac{" + (LaTeX[bKlammer]) + "}{2\cdot " + (LaTeX[aKlammer]) + "}\right)^2 +" + (LaTeX[cKlammer]) + ""
Text9: "\color{red}x_0 = " + (LaTeX[x0]) + ""
X: (x0 | 0)
Y: (0 | y0)
Text10: "\color{purple} y_0 = " + (LaTeX[y0]) + ""
d = false
Text11: "" + (If[d, "NF", "SF"]) + ""
yPosNF: 50
yPosUmwandlung: yPosNF + 120
xPosUmwandlung: 15
xPosNF: 15
xPosSF: 15
yPosSF: yPosNF + 360
e = false
x1 = 1 (slider from -5 to 5, step 0.1)
y1 = 1.5 (slider from -5 to 5, step 0.1)
a1 = 0.5 (slider from -5 to 5, step 0.1)
g(x) = (a1 * (x - x1)^(2)) + y1
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]) + ")")
Text15: "\color{black} f(x) = \color{rgb(0,0.6,1)}\underbrace{ " + (LaTeX[a1Klammer]) + "}_{a} \color{black}(x - \color{red}\underbrace{" + (LaTeX[x1Klammer]) + " }_{x_0} \color{black})^2 + \color{purple}\underbrace{" + (LaTeX[y1Klammer]) + " }_{y_0} "
Text8: "f(x) =   \color{rgb(0,0.6,1)}\underbrace{" + (LaTeX[aKlammer]) + " }_{a} \color{black}  \left( x - \color{red} \underbrace{\frac{-" + (LaTeX[bKlammer]) + "}{2 \cdot" + (LaTeX[aKlammer]) + "}}_{x_0}\color{black}\right)^2 +\color{purple}\underbrace{ " + (LaTeX[cKlammer]) + "- \frac{" + (LaTeX[bKlammer]) + "^2 }{4\cdot " + (LaTeX[aKlammer]) + " }}_{y_0}"
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]) + ""
Text21: "f(x) = " + (LaTeX[a1Klammer]) + " \cdot (x^2 - 2 \cdot " + (LaTeX[x1Klammer]) + " \cdot x + " + (LaTeX[x1Klammer]) + "^2) + " + (LaTeX[y1Klammer]) + ""
Text22: "f(x) = " + (LaTeX[a1Klammer]) + " x^2 - " + (LaTeX[a1Klammer]) + "\cdot 2 \cdot " + (LaTeX[x1Klammer]) + "\cdot x + " + (LaTeX[a1Klammer]) + "\cdot " + (LaTeX[x1Klammer]) + "^2 + " + (LaTeX[y1Klammer]) + ""
h = false
Text16: "f(x) = \color{rgb(0,0.6,1)}\underbrace{ " + (LaTeX[a1Klammer]) + " }_{a}\color{black}x^2 + \color{rgb(1,0.4,0)}\underbrace{((-2)\cdot " + (LaTeX[a1Klammer]) + "\cdot " + (LaTeX[x1Klammer]) + ")}_{b} \color{black }x + \color{rgb(0.4,0.6,0)}\underbrace{(" + (LaTeX[a1Klammer]) + "\cdot " + (LaTeX[x1Klammer]) + "^2 + " + (LaTeX[y1Klammer]) + ")}_{c}"
S: (x1 | y1)