$\begin{array} { l }a=4,& b=8\end{array}$
Find the $x$-coordinate of the vertex by substituting $a=4$ and $b=8$ into $x=-\frac{ b }{ 2a }$$x=-\frac{ 8 }{ 2 \times 4 }$
Solve the equation for $x$$x=-1$
Find the $y$-coordinate of the vertex by evaluating the function for $x=-1$$\begin{array} { l }f\left( x \right)=4{x}^{2}+8x-5,& x=-1\end{array}$
Calculate the function value for $x=-1$$f\left( -1 \right)=-9$
The vertex of the graph of the quadratic function is at $\left( -1, -9\right)$$\left( -1, -9\right)$