Answer
$f(x) =4(x+0.625)^2-21.5625$
Work Step by Step
The conversion of the function to the standard vertex form is self explanatory. All mathematical steps are shown below. $$
\begin{aligned}
f(x)&=4 x^2+5 x-20\\
& = 4\left(x^2+1.25 x\right) -20 \\
& = 4\left[x^2+1.25 x+\left( \frac{1.25}{2} \right)^2 \right]-20-4\cdot \left( \frac{1.25}{2} \right)^2 \\
& =4(x^2+1.25 x+0.625^2)^2-20-4\cdot 0.625^2\\
&= 4(x+0.625)^2-21.5625
\end{aligned}
$$
