The height of the object at the time of launch is 100 meters.
To find this, we simply have to put 0 in for x, as this is when there has been no time (at launch)
h(x)=-5(x-4)^2+180
h(0)=-5(0-4)^2+180
h(0)=-5(-4)^2+180
h(0)=-5(16)+180
h(0)=-80+180
h(0) = 100