Scheitelpunktform

Linearfaktorform

Polynomform

a = 1 (slider from -10 to 10, step 0.1)
x_s = 2 (slider from -10 to 10, step 0.1)
y_s = 3 (slider from -10 to 10, step 0.1)
f_{sp}(x) = (a * (x - x_s)^(2)) - y_s
S_{sp} = Extremum(f_{sp})
spf = true
lff = false
pyf = false
N_{sp1}, N_{sp2} = Root(f_{sp})
S_{spY}: (0, f_{sp}(0))
x_{N1} = -3 (slider from -10 to 10, step 0.05)
x_{N2} = 2 (slider from -10 to 10, step 0.05)
f_{lff}(x) = ((a * (x - x_{N1})) * (x - x_{N2}))
N_{lff1}, N_{lff2} = Root(f_{lff})
S_{lffY}: (0, f_{lff}(0))
S_{lff} = Extremum(f_{lff})
b = 2 (slider from -10 to 10, step 0.05)
c = -4 (slider from -10 to 10, step 0.05)
f_{pyf}(x) = (a * x^(2)) + (b * x) + c
N_{pyf1}, N_{pyf2} = Root(f_{pyf})
S_{pyfY}: (0, f_{pyf}(0))
S_{pyf} = Extremum(f_{pyf})