SOLUTION: A plastic hoop is thrown upward from the top of a 240-foot high building at a speed of 136 feet per second. The plastic hoop's height above ground can be modeled by the equation Hb

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Question 1138998: A plastic hoop is thrown upward from the top of a 240-foot high building at a speed of 136 feet per second. The plastic hoop's height above ground can be modeled by the equation Hbracket(t)=-16t^2+136t+240.
What is the maximum height of the plastic hoop? feet

Answer by ikleyn(52914) About Me  (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 = -b%2F%282a%29.


In this case, the maximum height is achieved at  t = -136%2F%282%2A%28-16%29%29 = 4.25 seconds.   


The maximum height is equal to the value of the given function  h(t) at t= 4.25 :


    h%5Bmax%5D = -16%2A4.25%5E2+%2B+136%2A4.25+%2B+240 = 529 ft.    ANSWER

Solved.

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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.