Aprojectile is thrown upward so that its distance above the ground after t seconds is given by the function h(t) = - 16t^2 + 576t. after how many seconds does the projectile take to reach its maximum height? show your work for full credit.

We  have to find te vertex of this parabola.
Given a square function:
F(x)=ax²+bx+c
The vertex of this parabola will be the point (-b/2a, f(-b/2a)

In this case:
h(t)=-16t²+576t
a=-16
b=576
-b/2a=-576/-32=18
h(18)=-16(18)²+576(18)=-5184+10368=5184
The vertex will be: (18, 5184)

Because a is negative we have a maximum, if a were positive we have a minimum.
Then we have a minimum at t=18 s; and the maximum heigth would be 5184 m

The projectile take to reach its maximum heigth in 18 s, and the maximum height would be 5184 m.

The answer you are looking for is right in front of you it’s c. 3/20