SOLUTION: Nicks height above the water t seconds after diving from a diving board into a pool can be modeled by f(t) = -4.9t2 + 4.9t + 5. What is Nicks maximum height above the water?

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Question 1126657: Nicks height above the water t seconds after diving from a diving board into a pool can be modeled by f(t) = -4.9t2 + 4.9t + 5. What is Nicks maximum height above the water?
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
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For a quadratic function  f(t) = at^2 + bt + c  with the negative leading coefficient  a < 0,  the maximal value is achieved at  t = .


In your case, the maximum is achieved at  t =  = 0.5 seconds.


The maximum value of the function (which is the maximal height under the question) is


     = -4.9*0.5^2 + 4.9*0.5 + 5 = 6.225 meters.

Since I am very smart, I was able to restore the unit of length as meters, even though the problem did not state it explicitly.

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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


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".


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