Given the parabola $y=a x^{2}+b x+c$ passes through $(c, 2)$, and $a|a|+b|b|=0$, also $a x^{2}+b x+c$ $-2>0$ has no solution. Try to find the values of $a, b, c$.
一、Prompt: The parabola is below $y=2$ and is tangent to $y$ $=2$ at the point $(c, 2)$. $(a=-6, b=6, c=$ $\frac{1}{2}$ )