If a baseball is projected upward from ground level with an initial velocity of 64 feet per second, then it’s height is a function of time, given by s= -16t^2+64t. What is the maximum height reached by the ball?

The maximum height is 64 feet and it occurs at 2 seconds.

A polynomial is an expression consisting of the operations of addition, subtraction, multiplication of variables. There are different types of polynomials such as linear, quadratic, cubic, etc.

A quadratic equation is of degree two and it has only two solution.

Given that  s= -16t²+64t

The maximum height is at ds/dt = 0

Hence:

ds/dt = -32t + 64

-32t + 64 = 0

32t = 64

t = 2 seconds

The maximum height is at 2 seconds, hence:

Maximum height = -16(2)² + 64(2) = 64 feet

The maximum height is 64 feet and it occurs at 2 seconds.

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  64 ft

Step-by-step explanation:

The equation can be factored as ...

  s = -16t(t -4)

This is the equation of a downward-opening parabola with t-intercepts of 0 and 4. The maximum height is at the vertex, halfway between those values, at t=2. At that time, the height is ...

  s = -16(2)(2-4) = 64 . . . . feet