what is the explicit equation for the terms (1,6) (2,18) (3,54)

what is the explicit equation for the terms (1,6) (2,18) (3,54)

$$\boxed{y=ax^2+bx+c}\\ \begin{array}{lrcl} (1): & \quad 6 &=& a*1^2+b*1 +c \\ (2): & \quad 18 &=& a*2^2+b*2 +c \quad | \quad : 2 \\ (3): & \quad 54 &=& a*3^2+b*3 +c \quad | \quad : 3 \\ \hline (1): & \quad 6 &=& 1a+b + c \\ (2): & \quad 9 &=& 2a+b +\frac{1}{2} c \\ (3): & \quad 18 &=& 3a+b +\frac{1}{3} c \\ \hline I: (2)-(1): & 9-6=3 &=& 2a+b +\frac{1}{2}c-(1a+b+c) = a -\frac{1}{2} c\\ II: (3)-(2): & 18-9=9 &=& 3a+b +\frac{1}{3}c-(2a+b+\frac{1}{2}c)= a -\frac{1}{6}c\\ \hline II-I: & 9-3=6 &=& a-\frac{1}{6}c-(a-\frac{1}{2}c) = \frac{1}{3}c \\ \textcolor[rgb]{1,0,0}{c} &\textcolor[rgb]{1,0,0}{=}& \textcolor[rgb]{1,0,0}{18}\\ \hline I: & 3 &=& a - \frac{1}{2}18 = a-9 \\ \textcolor[rgb]{1,0,0}{a} &\textcolor[rgb]{1,0,0}{=}& \textcolor[rgb]{1,0,0}{12}\\ \hline (1): & 6 &=& 12 + b + 18 = 30 + b \\ \textcolor[rgb]{1,0,0}{b} &\textcolor[rgb]{1,0,0}{=}& \textcolor[rgb]{1,0,0}{-24}\\ \end{array} \\ \boxed{y=12x^2-24 x+18 }\\$$

y = (2)3^x    where x in an integer > 0