2715.sagews

R = PolynomialRing(QQ, 'x')
f = R.lagrange_polynomial([(-2,1),(1,-1),(2,4)]); 
p1=plot(f,-5,5)
p2=point(((-2,1),(1,-1),(2,4)), rgbcolor=hue(1), size=30)
(p1+p2).show(ymax = 10, ymin = -10)
expand(f)

17/12*x^2 + 3/4*x - 19/6

R = PolynomialRing(QQ, 'x')
f = R.lagrange_polynomial([(-2,1),(0,1),(4,1)]);
p1=plot(f,-5,5)
p2=point(((-2,1),(0,1),(4,1)), rgbcolor=hue(1), size=30)
show(p1+p2)
expand(f)

1

R = PolynomialRing(QQ, 'x')
f = R.lagrange_polynomial([(-1,1),(3,2),(4,3),(5,-2)]);
p1=plot(f,-10,10)
p2=point(((-1,1),(3,2),(4,3),(5,-2)), rgbcolor=hue(1), size=30)
(p1+p2).show(ymax = 10, ymin = -10)
expand(f)

-21/40*x^3 + 33/10*x^2 - 107/40*x - 11/2