Asoftball is tossed into the air upward from a first floor balcony. the distance of the ball 14 +32t -16t^2 above the ground at any time is given by the function, the softball above the ground (in feet) and t is the time (in seconds) what was the maximum in feet, after t was thrown? where h() is the height of

You can either find the roots of the quadratic formula using the quadratic formula two find the halfway point or you can use the formula t=-b/2a.  Both of the two methods gives you the axis of symmetry (the t value for the vertex).
I will use the second method since I don't like using the quadratic formula.
t=-32/(2x-16)
t=1 second
After you find the t value for the axis of symmetry, you plug it into the formula of the graph to find the height.
h=-16+32+14
h=30 feet

40 & 50 in the right corner are the complementary angles as when placed in a sum (added together) they make 90°