Question 1166280
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<pre>

(a)  To answer this question, solve equation

         h(t) = 0 = 80t - 16t^2.


     The solution is  t = {{{80/16}}} = 5 seconds.




(b)  The function  H(t) = -16t^2 + 80t  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))}}} = 2.5.


    So, the ball gets the maximum height  2.5 seconds after is hit straight up. 




(c)  To find the maximum height, calculate h(t) at t = 2.5 seconds.

         {{{h[max]}}} = -16*2.5^2 + 80*2.5 = 100 ft.
</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.


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