Question 28313
you have 3 points that are on a quadratic curve, (-1,1),(1,5), and (2,10).


If you put x=-1 into the quadratic, the answer for y is 1...this is the coordinate (-1,1). Similarly when x=1, then y=5 and also when x=2, then y=10.


We do not know the quadratic, so we are going build it up from first principles...


the quadratic is of the form {{{y=ax^2 + bx + c}}}


so using (-1,1) gives a-b+c=1
and using (1,5) gives a+b+c=5
and using (2,10) gives 4a+2b+c=10


these are your three "p"'s.


--> got 3 polynomials in 3 unknowns --> a,b,c.


matrix is {{{(matrix(3,4,
1,-1,1,1,
1,1,1,5,
4,2,1,10) )}}}


the columns are the coefficients of a,b and c respectively and the y-value.
the rows are the 3 equations.


OK, now you use Gaussian Elimination (GE) to get the matrix M'...look into your books for this. I hate GE - i spent years doing it at uni.


I have done GE for you... you struggle with it. It is the only way!
c=2
b=2
a=1



and i have checked the quadratic with the 3 sets of coordinates...they match.



jon.