Are you familiar with matrices?

Compose the Vandermonde matrix for the t_i data, that is:

[ 1 t_1 t_1^2 ]

[ 1 t_2 t_2^2 ]

X = [ . . . ]

[ . . . ]

[ 1 t_n t_n^2 ]

Then compute:

(X^t X)^-1 X

and multiply this (from the left of course) by:

[ y_1 ]

Y = [ . ]

[ y_n ]

then the answer will be a vector consisting of the coefficients:

[ b ]

[ C2 ]

[ C1 ]

Compose the Vandermonde matrix for the t_i data, that is:

[ 1 t_1 t_1^2 ]

[ 1 t_2 t_2^2 ]

X = [ . . . ]

[ . . . ]

[ 1 t_n t_n^2 ]

Then compute:

(X^t X)^-1 X

and multiply this (from the left of course) by:

[ y_1 ]

Y = [ . ]

[ y_n ]

then the answer will be a vector consisting of the coefficients:

[ b ]

[ C2 ]

[ C1 ]