.
It is about finding the maximum of the quadratic function
h(t) = -at^2 + bt + c.
The maximum is reached at t= - .
In your case, a= -16, b= 64.
Therefore, the answer to the problem's question is
t = - = = 2 seconds.
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.
On solving similar problems to yours in this post, 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.