Becky1979
contestada

A ball 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

Respuesta :

irspow
The axis of symmetry is the x coordinate of the vertex and the absolute maximum/minimum value of f(x) is at the y-coordinate of the vertex of a parabola or quadratic function of the form ax^2+bx+c

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
ardni313

The time taken to reach the maximum height = 3 s

Further explanation

Quadratic function is a function that has the term x²

The quadratic function forms a parabolic curve

The general formula is

f (x) = ax² + bx + c

where 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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