Question 1158668
H=-16t^2+38t+101 
It helps to draw this.
The value of t at the highest point is where t=-b/2a, and b is 38 and a=-16
That will occur when t=-38/-32 seconds or 1.1875  or 1.19 seconds

Put that value of t bad into the equation
-16(1.1875^2)+38(1.1875)+101=-22.5625+45.125+101=123.5625 or 123.56 feet

set the equation = to 0 and solve using the quadratic formula. I will rewrite with a positive coefficient of the first term: 16t^2-38t-101=0
t=(1/32)(38+/- sqrt 1444+6464; sqrt term =88.93
the positive root is t=(126.93/32)=3.97 seconds
{{{graph(300,300,-5,6,-25,150,-16x^2+38x+101)}}}