calc-017-interpolacion-cuadratica

x

A

B

C

f(x)=ax^2+bx+c

Parábola de interpolación

B: (2, 3)
P = Point(xAxis)
yb: y(B)
xb: x(B)
A = (8, 4)
ya: y(A)
xa: x(A)
C: (3, 6)
xc: x(C)
detA: (xa^(2) * xb) + (xb^(2) * xc) + (xc^(2) * xa) - (xc^(2) * xb) - (xb^(2) * xa) - (xa^(2) * xc)
yc: y(C)
detz: ((xa^(2) * xb) * yc) + ((xb^(2) * xc) * ya) + ((xc^(2) * xa) * yb) - ((xc^(2) * xb) * ya) - ((xb^(2) * xa) * yc) - ((xa^(2) * xc) * yb)
cc: detz / detA
dety: (xa^(2) * yb) + (xb^(2) * yc) + (xc^(2) * ya) - (xc^(2) * yb) - (xb^(2) * ya) - (xa^(2) * yc)
bb: dety / detA
detx: (ya * xb) + (yb * xc) + (yc * xa) - (yc * xb) - (yb * xa) - (ya * xc)
aa: detx / detA
f(x) = (aa * x^(2)) + (bb * x) + cc
CasillaDeEntrada1 = Textfield(A)
CasillaDeEntrada2 = Textfield(B)
m: (y(B) - y(A)) / (x(B) - x(A))
n: y(A) - (m * x(A))
fx: f(x(P))
D: (x(P), fx)
b = Segment(D, P)
c = OrthogonalLine(D, yAxis)
E = Intersect(c, yAxis)
d = Segment(D, E)
texto1: "" + (LaTeX[ya]) + "  =a(" + (LaTeX[xa]) + ")^2+b(" + (LaTeX[xa]) + ")+c\\   " + (LaTeX[yb]) + "=a(" + (LaTeX[xb]) + " )^2+b(" + (LaTeX[xb]) + " )+c\\   " + (LaTeX[yc]) + "=a( " + (LaTeX[xc]) + " )^2+b(  " + (LaTeX[xc]) + ")+c"
CasillaDeEntrada3 = Textfield(C)
xp: x(P)
texto2: "f(x)=(" + (LaTeX[aa]) + ")x^2+(" + (LaTeX[bb]) + ")x+(" + (LaTeX[cc]) + ")\\f(" + (LaTeX[xp]) + ")=" + (LaTeX[fx]) + ""
a = false

Tool: Inc
Input: A, B, C, D, E
Output: F

c = Ellipse(A, B, C)
a = Ray(D, E)
F = Intersect(c, a, 1)

Tool: Ref
Input: A, B, C, D, E
Output: G

c = Ellipse(A, B, C)
u = Vector(D, E)
a = Ray(D, E)
F = Intersect(c, a, 1)
b = Tangent(F, c)
F' = Translate(F, u)
v = Vector(F, F')
v' = Mirror(v, b)
G: F + v'