Question

you have 9 terms, the first is 0 and the 9th is 12 one of the outputs is 27 what is the equation for the pattern?

Answer 1

y = (-13x^2 + 119x)/60

your 9 terms are obtained by letting
x = 0,1,2,..,8

check:
let x=0, yterm = 0
let x=5, yterm = 27
let x=8, yterm = 12

The above equation of course is not unique, I simply decided I wanted a quadratic, and I "forced" your result of 27 to be the output of an input of 5, and decided to make (5,27) one of the points. The other two points would be (0,0) and (8,12)

so my equation would be
y = ax^2 + bx , I then subbed in the points (5,27) and (8,12)

This gave me 2 equations in 2 unknowns, which I solved to get my result

Answer 2

the denominator of my equation should have been 10, not 60

so

y = (-13x^2 + 119x)/10