Question 1114527
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<pre>
The height of the ball over the ground is described by a quadratic function


h(t) = - 16*t^2 + 32t + 20.    (1)


The maximum height is achieved when the quadratic function (1) has the maximum.


From algebra, the quadratic function  y = ax^2 + bx + x has extremum at x = {{{-b/(2a)}}}.


In your case,  a= -16,  b= 32,  so  x= {{{-32/(2*(-16))}}} = 1.


Thus the quadratic function (1) achieved maximum at t = 1. It means that the ball will achieve the maximum height at t= 1 seconds.


And the maximum height will be h(1) = -16*1^2 + 32*1 + 20 = 36 ft.


<U>Answer</U>.  The ball will achieve its maximum height of 36 ft in 1 second.
</pre>

Solved.


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On finding the maximum/minimum of a quadratic function see the lessons in this site

&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>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/OVERVIEW-of-lessons-on-finding-the-maximum-minimum-of-a-quadratic-function.lesson>OVERVIEW of lessons on finding the maximum/minimum of a quadratic function</A>


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this textbook under the topic "<U>Finding minimum/maximum of quadratic functions</U>". 



Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.