One, (20 points) Let the quadratic function be $y=a x^{2}+b x+c$. The graph is above the line $y=-2 x$ if and only if $1<x<3$.
(1) If the equation $a x^{2}+b x+6 a+c=0$ has two equal real roots, find the expression of the quadratic function;
(2) If the maximum value of the quadratic function is positive, find the range of values for $a$.
(1) From the problem, we know that $x=1$ and 3 are the roots of the equation $a x^{2} +b x+c=-2 x$, and $a0$.

Also $a0$.
Then $(-4 a-2)^{2}-4 a(3 a)>0$
$$
\Rightarrow a<-2-\sqrt{3} \text { or }-2+\sqrt{3}<a<0 \text {. }
$$