Question

Can someone show me how to complete the square of: \[f(t) = -16t^2 - 32t + 128\]

Answer 1

\[\begin{align*}
f(t)&=-16t^2-32t+128\\\\
&=-16\left(t^2+2t\right)+128\\\\
&=-16\left(t^2+2t\color{red}{+1-1}\right)+128\\\\
&=-16\left((t+1)^2-1\right)+128\\\\
&=-16(t+1)^2+16+128\\\\
&=-16(t+1)^2+144
\end{align*}\]