8. Let the quadratic function $f(x)=a x^{2}+b x+c$, when $x=3$ it has a maximum value of 10, and the length of the segment it intercepts on the $x$-axis is 4, then $f(5)=$ $\qquad$ .
8. $f(5)=0$ Let $f(x)=a(x-3)^{2}+10$, set $f(x)=0$, the two roots are $x_{1}, x_{2}$, by Vieta's formulas $\left(x_{1}+x_{2}\right)^{2}-$ $4 x_{1} x_{2}=16,6^{2}-4 \frac{9 a+10}{a}=16$, thus $a=-\frac{5}{2}$.