Chapter 10 - The Laplace Transform and Some Elementary Applications - 10.5 The First Shifting Theorem - Problems - Page 694: 4

$t^2+2t$

We are given that $f(t)=t^2-2t$ and $a=-2$ When $a$ has a positive value then , shift the function to the right for $a$ units and when $a$ has a negative value then , shift the function to the left for $a$ units Now, $f(t-a) =f(t+2) \\=(t+2)^2-2(t+2)\\=t^2+4t+4-2t-4\\=t^2+2t$