Question 1000335
With gravity, these are usually -16t^2 functions, because gravity is -32 ft/sec^2, and the formula has a half in it.  There is force behind the ball, yet unknown, and there is a +64, which is the feet above ground.
-16t^2+ bt+64=0, when t=4
-256+4b+64=0
4b=-192
b=48

This is the equation: f(t)= -16t^2+48t+64.
Check this.  
At t=0, the ball is 64 feet off the ground
At 4 seconds, -256+48(4)+64=0
The highest point time value is -b/2a=-48/-32=1.5 seconds.  
f(1.5)=-16(2.25)+48(1.5)+64=-36+136=100 feet, the vertex.
{{{graph(300,200,0,5,-10,125,-16x^2+48x+64)}}}