Question 1149032
.
a fastball is hit straight up over home plate.  the balls height, H( in feet), from the ground is modeled 
by the quadratic function defined by  H(t)=16^t2+80t+5 where t is measured in seconds.  
at what time did the fastball reach the maximum height?  solve algebraically
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            First, the function  H(t)  in your post is written  INCORRECTLY,  having a  FATAL  error.


            The correct form of this function is   H(t) = -16t^2 + 80t + 5.


            Notice the sign  " - "  (minus)  before  16t^2     (!)


            With the corrected formula,  see my solution below.



<pre>
The function  H(t) = -16t^2 + 80t + 5  is a quadratic function, whose plot is a parabola opened down.


This quadratic function has the maximum at the value of its argument  t = {{{-b/(2a)}}}, where "a" is the coefficient at t^2

and "b" is the coefficient at t.


In your case, a= -16,  b= 80, so the function gets the maximum at  t = {{{-80/(2*(-16))}}} = 3.5.


So, the fastball gets the maximum height  2.5 seconds after is hit straight up. <U>ANSWER</U>
</pre>

Solved.


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On finding the maximum/minimum of a quadratic function, &nbsp;see the lessons 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>HOW TO complete the square to find the minimum/maximum of a quadratic function</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-How-to-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>Briefly on finding the minimum/maximum of a quadratic function</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-to-find-the-vertex-of-a-quadratic-function.lesson>HOW TO complete the square to find the vertex of a parabola</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-finding-the-vertex-of-a-parabola.lesson>Briefly on finding the vertex of a parabola</A>

in this site.


On solving similar problems to yours in this post, &nbsp;see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Problem-on-a-projectile-moving-vertically.lesson>Problem on a projectile moving vertically up and down</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Problem-on-projectile-shooted-vertically-upward.lesson>Problem on an arrow shot vertically upward</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Typical-problems-on-an-projectile-moving-vertically-up-and-down.lesson>Problem on a ball thrown vertically up from the top of a tower</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Problem-on-a-toy-rocket-launched-vertically-up--from-the-top-of-a-platform.lesson>Problem on a toy rocket launched vertically up from a tall platform</A>

in this site.