Solving a quadratic Lagrange interpolant , How ?

[uaeXuae]

http://img151.imageshack.us/img151/5562/updatequicklyte1.jpg



how would i solve it using MATLAB ? I tried many times but i didnt get the same answer may anyone help me please ?

 

[uaeXuae]

Anyone please ? I have to submit this in 2 days please help...


My attempt is as follows

v(15)=a0+a1(t)+a2(t)=24
a0+a1(15)+a2(15)^2=24


v(18)=a0+a1(t)+a2(t)=37
a0+a1(18)+a2(18)^2=37

v(22)=a0+a1(t)+a2(t)=25
a0+a1(22)+a2(22)^2=25


I then wrote it in the Matrix Form

a=[1 15 225;1 18 324;1 22 484]
b=[24;27;35]
x=a/b

Results:

a0=-323.8571
a1=38.9048
a2=-1.0476


Using the following Equation:

v(16)=-323.8571+(38.9048*16)+(-1.0476*(16^2))=
30.4341 s which is wrong ofcourse The ans is 20.846 so wheres my mistake

 

[uaeXuae]

The value 26m/s is obtained twice

First interval: 15 -18
Second Interval: 18-22

So i should be getting two answers is that so ?

 

[uaeXuae]

Anyone please help me submission is tommrow