we get that the x coordinate of the vertex is
[tex]\frac{-8}{2a}=1\rightarrow2a=-8\rightarrow a=-\frac{8}{2}=-4[/tex]
and if we replace 1 in the function we get 9. So
[tex]\begin{gathered} -4\cdot1+8\cdot1+c=9\rightarrow-4+8+c=9 \\ 4+c=9\rightarrow c=9-4=5 \end{gathered}[/tex]
so we get that a=-4 and c=5
