y = 2x²-4x

y = -2x²+4x

Parabola d'equazione
      y = 2x² - 4x

\begin{array}{}  y = 0 \ per \; x= 0 \; o \; x = 2  \end{array}  

\begin{array}{}  y < 0 \ per \; 0<x< 2  \end{array}  

\begin{array}{}  y > 0 \ per \; x<0 \end{array}  

Parabola d'equazione
      y = -2x² + 4x

\begin{array}{}  y > 0 \ per \; 0<x<2  \end{array}  

\begin{array}{}  y < 0 \ per \; x<0  \end{array}  

\begin{array}{}  y = 0 \ per \; x= 0 \; o \; x = 2  \end{array}  

\begin{array}{}  y > 0 \ per \; x>2 \end{array}  

\begin{array}{}  y < 0 \ per \; x>2  \end{array}  

t = -0.75 (slider from -0.75 to 2.75, step 0.1)
d = true
e = false
B: (t, (2 * t^(2)) - (4 * t))
C: (t, (2 * t^(2)) - (4 * t))
A, O = Intersect(c, xAxis)
a = OrthogonalLine(B, xAxis)
D = Intersect(xAxis, a)
b = Segment(B, D)
g(x) = If[0 < x < 2, (2 * x^(2)) - (4 * x)]
F: (t, (2 * t^(2)) - (4 * t))
i = OrthogonalLine(F, xAxis)
G = Intersect(xAxis, i)
j = Segment(F, G)
f(x) = If[x < 0, (2 * x^(2)) - (4 * x)]
h(x) = If[x > 2, (2 * x^(2)) - (4 * x)]
k = OrthogonalLine(C, xAxis)
E = Intersect(k, xAxis)
c' = Mirror(c, xAxis)
m(x) = If[x < 0, (-2 * x^(2)) + (4 * x)]
n(x) = If[0 < x < 2, (-2 * x^(2)) + (4 * x)]
p(x) = If[x > 2, (-2 * x^(2)) + (4 * x)]
B' = Mirror(B, xAxis)
B'_1 = Mirror(B, xAxis)
D' = Mirror(D, xAxis)
b' = Segment(B'_1, D')
q = Segment(C, E)
r = Segment(O, A)
l = Ray(O, D)
s = Ray(A, G)
a_1 = Ray(O, D')
C' = Mirror(C, xAxis)
E' = Mirror(E, xAxis)
q' = Segment(C', E')
b_1 = Segment(O, A)
F' = Mirror(F, xAxis)
G' = Mirror(G, xAxis)
j' = Segment(F', G')
c_1 = Ray(A, E')