Quadratische Funktion - Scheitelpunktform

x_0

y_0

$x_0$

Neu

$a$

$y_0$

yPosNF: 50
xPosNF: 15
xPosSF: 15
yPosSF: yPosNF + 360
x0 = 0 (slider from -5 to 5, step 0.1)
y0 = -1.5 (slider from -5 to 5, step 0.1)
a = 1 (slider from -5 to 5, step 0.1)
f(x) = (a * (x - x0)^(2)) + y0
b1: ((2 * a) * x0)
c1: (a * x0^(2)) + y0^(2)
aKlammer = If(a ≥ 0, LaTeX[a], "(" + (LaTeX[a]) + ")")
x0Klammer = If(x0 ≥ 0, LaTeX[x0], "(" + (LaTeX[x0]) + ")")
y0Klammer = If(y0 ≥ 0, LaTeX[y0], "(" + (LaTeX[y0]) + ")")
Text15: "\color{black} f(x) = \color{rgb(0,0.6,1)}\underbrace{ " + (LaTeX[aKlammer]) + "}_{a} \color{black}(x - \color{red}\underbrace{" + (LaTeX[x0Klammer]) + " }_{x_0} \color{black})^2 + \color{purple}\underbrace{" + (LaTeX[y0Klammer]) + " }_{y_0} "
t1 = 1 (slider from 1 to schritte + 1, step 1)
minA = Min(a, 1)
maxA = Max(a, 1)
schritte: 20
x0Iteration = If(x0 ≟ 0, Sequence[0, i, 1, schritte + 1], Sequence[i, i, 0, x0, (x0 - 0) / schritte])
y0Iteration = If(y0 ≟ 0, Sequence[0, i, 1, schritte + 1], Sequence[i, i, 0, y0, (y0 - 0) / schritte])
aIteration = If(a ≟ 1, Sequence[1, i, 1, schritte + 1], Sequence[i, i, 1, a, (a - 1) / schritte])
t2 = 1 (slider from 1 to schritte + 1, step 1)
t3 = 1 (slider from 1 to schritte + 1, step 1)
h(x) = (Element[aIteration, t2] * (x - Element[x0Iteration, t1])^(2)) + Element[y0Iteration, t3]
t1Klammer = If(t1 ≥ 0, LaTeX[t1], "(" + (LaTeX[t1]) + ")")
t2Klammer = If(t2 ≥ 0, LaTeX[t2], "(" + (LaTeX[t2]) + ")")
t3Klammer = If(t3 ≥ 0, LaTeX[t3], "(" + (LaTeX[t3]) + ")")
Text1: "\color{darkgreen} h(x) \color{black }= \color{rgb(0,0.6,1)}\underbrace{a}_{" + (LaTeX[Element[aIteration, t2]]) + "} \color{black}(x - \color{red}\underbrace{ x_0 }_{" + (LaTeX[Element[x0Iteration, t1]]) + "} \color{black})^2 + \color{purple}\underbrace{y_0}_{" + (LaTeX[Element[y0Iteration, t3]]) + "} "