SOLUTION: At a baseball game, workers toss T-shirts to spectators in the stands out of a sling-shot. The height of a T-shirt is modelled by the function h(t)=-5t^2+20t+1 where h(t) is height

Question 1137558: At a baseball game, workers toss T-shirts to spectators in the stands out of a sling-shot. The height of a T-shirt is modelled by the function h(t)=-5t^2+20t+1 where h(t) is height in metres and t is the time in seconds after the toss.
What is the maximum height of the T-shirt if it is not caught?
How much time does it take the T-shirt to reach maximum height?
Answer by ikleyn(52780) (Show Source): You can put this solution on YOUR website!
.

It is about the maximum value of a quadratic function.


The quadratic function  f(x) = ax^2 + bx + c of the general form with the negative leading coefficient a < 0

has the maximum value at  x = .


In this case, the maximum height is achieved at  t =  =  = 2 seconds.    ANSWER


The maximum height is equal to the value of the given function  h(t) at t= 2 :


     =  = -20 + 40 + 1 = 21 meters.    ANSWER

All questions are answered and the problem is solved.

----------------------

On finding the maximum/minimum of a quadratic function see the 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.

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".

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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