GAIC Math 2024 Problem 55

Given $f(x)$ and $g(x)$ are two quadratic functions with the coefficient of the quadratic term being 1 for both. If $g(6)=35,\frac{f(-1)}{g(-1)}=\frac{f(1)}{g(1)}=\frac{21}{20}$, then $f(6)=\_\_\_\_\_$.