The graph of a polynomial passes through points A(2,5), B(3,2), and C(5,-1) use Gaussian elimination to find the polynomial.

what is the best way to start?

Question

The graph of a polynomial passes through points A(2,5), B(3,2), and C(5,-1) use Gaussian elimination to find the polynomial. 

what is the best way to start?

anonymous · Answer

HELP!!

amistre64 · Answer

3 points, 3 unknowns ...

amistre64 · Answer

2^2 2 1  5
3^2 3 1  2
5^2 5 1 -1


 4  2  1   5
 9  3  1   2
25 5  1  -1

row reduce to your hearts content

anonymous · Answer

Ok thank you for the matrices but how did you get to that first step?

amistre64 · Answer

hmm, well we need to be able to fit these point to some curve.

2 points define a line, 3 points define a quadratic ...

we need some quadratic equation that satisfies:$$ax^2+bx+c=y$$for the stated points

$$2^2a+2b+1c=5$$$$3^2a+3b+1c=2$$$$5^2a+5b+1c=-1$$
then its just a matter of pulling off the coefficents to form the matrix

anonymous · Answer

That makes sense thank you very much! :)

amistre64 · Answer

youre welcome :)