If R=8, A=16, W=18, what is the formule for A to Z?

A=16, B=  , C=  , D=  , E=  , F=  , G=  ,
H=  , I=  , J=  , K=  , L=  , M=  , N=  ,
O=  , P=  , Q=  , R=8 , S=  , T=  , U=  , 
V=  , W=18, X=  , Y=  , Z=

Let f(1) = A,  f(2) = B, f(3) = C, ... 
    f(25) = Y, f(26) = Z

Given that 

R is the 18th letter and it is 8, so f(18) = 8
A is the 1st letter and it is 16, so f(1) = 16 
W is the 23rd letter and it is 18, so f(23) = 18

Substitute in the equation

f(x) = ax² + bx + c

f(18) =  8 = a(18)² + b(18) + c 
 f(1) = 16 = a(1)² + b(1) + c
f(23) = 18 = a(23)² + b(23) + c

324a + 18b + c =  8
   a +   b + c = 16
529a + 23b + c = 18

Solve that system of equations and 
get

a = 21/187, b = -487/187, 3458/187

So the formula is

f(x) = ax² + bx + c

f(x) = (21/187)x² - (487/187)x + 3458/187

f(x) = (21x² - 487x + 3458)/187

A=16, B=2568/187, C=2186/187, D=1846/187, E=1548/187,
F=76/11, G=98/17, H=906/187, I=776/187, J=688/187, 
K=642/187, L=58/17, M=676/187, N=756/187, O=878/176,
P=1942/187, Q=1248/187, R=8, S=1786/187, T=2118/187,
U=2492/187, V=2908/187, W=18, X=3866/187, Y=4408/187,
Z=4992/187

Edwin