SOLUTION: A ball is thrown into the air with an upward velocity. It’s height, h, after t seconds is given by the function below h=-16t+64t+960. How many seconds did it take for the ball to

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A ball is thrown into the air with an upward velocity. It’s height, h, after t seconds is given by the function below h=-16t+64t+960. How many seconds did it take for the ball to      Log On


   

Question 1171621: A ball is thrown into the air with an upward velocity. It’s height, h, after t seconds is given by the function below h=-16t+64t+960. How many seconds did it take for the ball to reach its maximum height?
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.

It is about finding the maximum of the quadratic function


    h(t) = -at^2 + bt + c.


The maximum is reached at t= - b%2F%282a%29.


In your case,  a= -16, b= 64.


Therefore, the answer to the problem's question is  


    t = - 64%2F%282%2A%28-16%29%29 = 64%2F32 = 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.