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A ball travels on a parabolic path in which the height (in feet) is given by the expression -16t^2+80t+21, where t is the time after launch. What is the maximum height of the ball, in feet?

ma931 Dec 26, 2018

#1**+1 **

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....

.tertre Dec 26, 2018