help please

Factoring:: \(-16t^2+80t+21=t=-\frac{1}{4},\:t=\frac{21}{4}\)

We first factor \(-16t^2+80t+21\) into \(-\left(4t+1\right)\left(4t-21\right)\)

Next, \(4t+1=0 \longrightarrow t=-\frac{1}{4}.\)

And, \(4t-21=0 \longrightarrow t=\frac{21}{4}.\)

Since the value has to be maximum, the answer is \(\boxed{\frac{21}{4}}.\)

Oh, I think I'm wrong....

-16t^2 + 80t + 21

The  t  that maximizes this is given by :

-80 / [ 2 * -16]  =  80 / 32  =  5/2

Putting this back into the function, we get that the max height is

-16(5/2)^2 + 80(5/2) + 21  =

-16(25/4) + 200 + 21  =

-100 + 200 + 21 =

121 ft