SOLUTION: The height(h) in feet of a ball(t) seconds after being tossed upward is given by the function h(t) = 80t - 16t^2. How long will it take to reach the maximum height?

Question 1187137: The height(h) in feet of a ball(t) seconds after being tossed upward is given by the function h(t) = 80t - 16t^2.
How long will it take to reach the maximum height?
Answer by ikleyn(52754) (Show Source): You can put this solution on YOUR website!
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The height(h) in feet of a ball(t) seconds after being tossed upward is given by the function h(t) = 80t - 16t^2.
How long will it take to reach the maximum height?
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I will show you very simple way to solve this problem.

You have a quadratic function; its plot is a parabola, inverted downward

    h(t) = 80t - 16t^2 = 16t(5 - t).


Its x-intercepts are  t= 0  and  t= 5.


The parabola has the maximum exactly half way between x-intercepts, i.e. the maximum is at  t =  =  = 2.5 seconds.


So, it will take 2.5 seconds to reach the maximum height.    ANSWER

Solved.

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There are other ways to solve this problem.

To see many other solved similar and different problems, see the lessons

    - Introductory lesson on a projectile thrown-shot-launched vertically up
    - Problem on a projectile moving vertically up and down
    - Problem on an arrow shot vertically upward
    - Problem on a ball thrown vertically up from the top of a tower
    - Problem on a toy rocket launched vertically up from a tall platform

Consider these lessons as your textbook, handbook, tutorials and (free of charge) home teacher.
Read them attentively and learn how to solve this type of problems once and for all.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Projectiles launched/thrown and moving vertically up and dawn".

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.

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