Need help

The maximum possible value of the expression occurs at the vertex of the graph. 

So let's find the y value of the vertex.

First, simplifying and combining all like terms, we get the equation

$4t^{2}+4t+14$

Now, the x value of the vertex of the graph is $\frac{-b}{2a}$, so we have

$\frac{-4}{8} = -1/2$

Plugging this value back into equation and subbing out t, we get

$y = 13$

So 13 is the our answer. 

Thanks! :)