The parabola with equation $y=ax^2+bx+c$ and vertex $(h,k)$ is reflected about the line $y=k$. This results in the parabola with equation $y=dx^2+ex+f$. In terms of $k$, what is the value of $a+b+c+d+e+f$?
To reflect a parabola about the line $y=k$, I need to replace $y$ with $2k-y$ in the original equation. This gives me $2k-y=ax^2+bx+c$. Rearranging this equation, I get $y=2k-ax^2-bx-c$. Comparing this with the equation of the reflected parabola, I see that $d=-a$, $e=-b$, and $f=2k-c$. Therefore, $a+b+c+d+e+f=a+b+c-a-b+2k-c=2k$. This is the answer, regardless of the values of $a$, $b$, $c$, $d$, $e$, and $f$. 