y = a x²

This geogebra file demonstrates the reflection properties
of a parabola. 

xval = -4 (slider from -4 to 4, step 0.01)
a = 0.25 (slider from 0.02 to 0.8, step 0.01)
f(x) = a * x^(2)
A: (xval, f(xval))
g(x) = f(x(A)) + f'(x(A)) * (x - x(A))
B: (x(A), 10)
b = Segment(B, A)
D: (x(A) - 2, g(x(A) - 2))
E: (x(A) + 2, g(x(A) + 2))
α = Angle(B, A, D)
E' = Rotate(E, α, A)
β = Angle(E, A, E')
c = Line(A, E')
C = Intersect(c, yAxis)
d = Segment(A, C)
text1: "b + d = " + (b + d)
list1 = Sequence(CurveCartesian[j / 10, t, t, -2, 24], j, -50, 50)