Aprojectile is thrown upward so that its distance above the ground after t seconds is h = -16t2 + 608t. after how many seconds does it reach its maximum height?

The question is asking you to find the axis of symmetry, which is the x-value of the vertex. In order to do that you need to factor the function to find the zeros and add the zeros together and divide by two to find the axis of symmetry.
y=-16x^2+608x
y=-16x(x-38)
Zeros: x=0 and x=38
38/2=19
Therefore it takes 19 seconds for the projectile to reach its maximum height.
Hope this helps!