h(t) = -16t^2 + 50t + 6

Extreme values of a parabola occur at the vertex, so 
the vertex formula:

The t-coordinate is found by the formula 

 =  =  or 1.5625 seconds.

That's the answer you were asked to find.


The h-coordinate is found by substituting the t-value
into the formula

h(t) = -16t^2 + 50t + 6

h = -16 + 50 + 6

the answer is 59.125 feet.  That's the highest point it reaches,
and it reaches that in 1.5625 seconds.

Edwin