Question 635476
  <pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
Note: the vertex form of a Parabola opening up(a>0) or down(a<0), {{{y=a(x-h)^2 +k}}} 
where(h,k) is the vertex  and  x = h  is the Line of Symmetry
h = - 16 t^2 + 12x + 10 
  {{{12/(2*16) = 3/8}}}
h = -16(x - 3/8) + 16(9/64) + 10 
h = -16(x - 3/8) + 9/4 + 40/4    \ parabola opening Downward  a = -16 < 0
h = -16(x - 3/8) + 49/4  Vmax(3/8, 12.25)
12.25 ft the maximum height that the ball will reach

{{{drawing(300,300, -6, 6, -15, 15,  blue(line(3/8,15,3/8,-15))  , grid(1),
circle(3/8, 12.25,0.3),
graph( 300, 300, -6, 6, -15, 15,0,-16x^2 + 12x + 10))}}}