Solve for: f(x)=4x^2+8x-5

Expression: $f\left( x \right)=4{x}^{2}+8x-5$

Identify the coefficients $a$ and $b$ of the quadratic function

$\begin{array} { l }a=4,& b=8\end{array}$

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 $\left( -1, -9\right)$

$\left( -1, -9\right)$