2716.sagews

x0=-2
y0=1
x1=1
y1=-1
x2=2
y2=4
L0=(((x-x1)*(x-x2))/((x0-x1)*(x0-x2)))
L1=(((x-x0)*(x-x2))/((x1-x0)*(x1-x2)))
L2=(((x-x0)*(x-x1))/((x2-x0)*(x2-x1)))
P=y0*L0+y1*L1+y2*L2
p1=plot(P,-10,10)
(p1).show(ymax = 10, ymin = -10)
expand(P)

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

x0=-2
y0=1
x1=0
y1=1
x2=4
y2=1
L0=(((x-x1)*(x-x2))/((x0-x1)*(x0-x2)))
L1=(((x-x0)*(x-x2))/((x1-x0)*(x1-x2)))
L2=(((x-x0)*(x-x1))/((x2-x0)*(x2-x1)))
P=y0*L0+y1*L1+y2*L2
p1=plot(P,-5,5)
(p1).show(ymax = 10, ymin = -10)
expand(P)

1

x0=-1
y0=1
x1=3
y1=2
x2=4
y2=3
x3=5
y3=-2
L0=(((x-x1)*(x-x2)*(x-x3))/((x0-x1)*(x0-x2)*(x0-x3)))
L1=(((x-x0)*(x-x2)*(x-x3))/((x1-x0)*(x1-x2)*(x1-x3)))
L2=(((x-x0)*(x-x1)*(x-x3))/((x2-x0)*(x2-x1)*(x2-x3)))
L3=(((x-x0)*(x-x1)*(x-x2))/((x3-x0)*(x3-x1)*(x3-x2)))
P=y0*L0+y1*L1+y2*L2+y3*L3
p1=plot(P,-10,10)
(p1).show(ymax = 10, ymin = -10)
expand(P)

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