Answer :
[tex]f(x)=-9x^2+7x+8\\\\a=-9;\ b=7;\ c=8\\\\x_{vertex}=\frac{-b}{2a}\\\\x_{vertex}=\frac{-7}{2\cdot(-9)}=\frac{-7}{-18}=\frac{7}{18}[/tex]
[tex]x_v=-\frac{b}{2a}\\
x_v=-\frac{7}{2\cdot(-9)}\\
x_v=\frac{7}{18}\\[/tex]