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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".