Aball is kicked upward with an initial velocity of 56 feet per second. the ball's height h (in feet) can be expressed as a function of time t (in seconds) by the equation h = -16t2 + 56t. how much time does the ball take to reach its highest point?

Answer is 1.75 seconds.

velocity is 0 at highest point, by taking the derivative of function we can get the time it takes before it reached its highest point

The equation of motion (for the height of the ball) is h(t) = -16t^2 + 56t.  Please note that you must use the symbol " ^ " to indicate exponentiation.

This quadratic function could be graphed easily.  Factoring h(t) = -16t^2 + 56t, we get h(t) = t(-16t + 56).  We can obtain the horiz. intercepts by setting this function equal to zero and solving for t.  One value is t=0; the other is t=(7/2).  If you graph this parabola, you can read off from your graph the t value at which the ball reaches its highest point.  That t value is halfway between t=0 and t=(7/2).

Alternatively, you could find the vertex of this parabola as a t-value.  This t-value is the answer to this problem.

Recall that at the vertex, t = -b/a, where, in this case, b=56 and a=-16.
Calculate: 

t = -56/(-16).  The units of measurement must be "sec."