50g

To solve your problem, first put your calculator in RPN mode and soft
menu (flag 117 set).
first enter a vector with the values of y. (wherever you see a space
pres the [SPC] key and notice LS Left Shift and RS Right Shift.)

LS[]3 8 12 ENTER

enter a vector with X^2 X and 1 and duplicate it.
LS[] 'X^2' 'X' 1 ENTER ENTER

enter X=1 and substitute this value in the vector.

'X=1' ENTER
RS ALG NXT SUBST

swap the contents in level 1 and level 2, duplicate the vector in
level 1, enter X=2 and substitute this value in the vector.

Press the right arrow of the cursor key to swap.
ENTER
'X=2' ENTER
SUBST

swap one last time, enter X=-2 and substitute this value in the
vector.

Press the right arrow of the cursor key to swap.
'X=-2' ENTER
SUBST

At this point you have four vectors in the stack, the last three are
rows of the matrix for the system. Let's form that matrix.

3
RS MTH MATRX ROW ROW->

to solve this system just press the divided by key, here we represent
it by /

/

the result is the vector [2 -1 2]

a=2, b=-1 and c=2

you can check the solution with the function PEVAL (Polynomial
EVALuation) you need the vector of coeficients in level 2 in this
case [2 -1 2] and the value of X (like 1) in level 1 and PEVAL find
the value of f(x).