SOLUTION: A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t)=48t-16t^2 After how long will it reach its maximum height?

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Question 1101446: A ball is thrown vertically upward. After t seconds, its height
h (in feet) is given by the function h(t)=48t-16t^2
After how long will it reach its maximum height?
Found 3 solutions by htmentor, Alan3354, ikleyn:
Answer by htmentor(1343)   (Show Source): You can put this solution on YOUR website!
The maximum height will be reached when dh/dt = 0
dh/dt = 48 - 32t = 0
This gives t = 1.5
Ans: 1.5 seconds
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
A ball is thrown vertically upward. After t seconds, its height
h (in feet) is given by the function h(t)=48t-16t^2
After how long will it reach its maximum height?
----------------
Without calculus:
The max is the vertex of the parabola.
That's at t = -b/2a = -48/-32 = 1.5 seconds
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
This question asks at which value of "t" the quadratic function

h(t) = 48 - 16*t^2 

reaches its maximum.


The general theory regarding a quadratic function of general form

y = ax^2 + bx + c

says that it reaches the maximum/minimum at x = .


So, in our case, the maximal height reaches at  t =  = 1.5 seconds.


-------------------
On finding maximum/minimum of a quadratic function see my lessons
    - HOW TO complete the square to find the minimum/maximum of a quadratic function
    - Briefly on finding the minimum/maximum of a quadratic function
    - HOW TO complete the square to find the vertex of a parabola
    - Briefly on finding the vertex of a parabola
in this site.

On a projectile thrown/shot/launched vertically up see the lessons
    - 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
in this site.


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  "Finding minimum/maximum of quadratic functions"
and 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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