An object is thrown upward with an initial velocity of 32 feet per second. the objects height is modeled by the function h(t) = - 16t^2 + 32t
where t is the time of the at height, h(t). what is the maximum height of the object?

Using calculus...

dh/dt=-32t+32

When velocity, dh/dt, is equal to zero, the object is at its maximum height.

dh/dt=0 only when 32t=32, t=1 second, so the maximum height is h(1)

h(1)=-16+32=16ft

Using algebra

The maximum height will occur at the midpoint between the two zeros of the height function because of a quadratics symmetry...

h(t)=0 when

-16t^2+32t=0

-16t(t-2)=0

so t=0 and 2

The midpoint is t=1

And of course this will give you the same as we found earlier.  The maximum height is h(1) ft

counselor more than or equal to 10 hours

Baby sitting more than or equal to 30 hours

Step-by-step explanation: