Aball is thrown vertically upward. after t seconds, its height h (in feet) is given by the function h(t)= 96t-16t^2 . after how long will it reach its maximum height? do not round your answer. time: seconds
The vertex will always have the coordinates:
x=-b/(2a) and y=(4ac-b^2)/(4a)
Since we only need to know the time when it reaches its maximum height we can simply solve for the x coordinate which is time in this circumstance. so:
t=-b/(2a)=-96/(-16*2)=3 seconds
The time taken to reach the maximum height = 3 s
Further explanationQuadratic function is a function that has the term x²
The quadratic function forms a parabolic curve
The general formula is
f (x) = ax² + bx + cwhere a, b, and c are real numbers and a ≠ 0.
The parabolic curve can be opened up or down determined from the value of a. If a is positive, the parabolic curve opens up and has a minimum value. If a is negative, the parabolic curve opens down and has a maximum value
So the maximum is if a <0 and the minimum if a> 0.
After t seconds, a ball height h (in feet) is given by the function h (t) = 96t-16t²
The maximum value of the function is obtained if the first derivative of the function h (t) = 0
96-32t = 0
96 = 32t
t = 3 s
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