Question 1162781
a+b+c=144
16a+4b+c=0

c=144-a-b=-16a-4b
15a+3b=-144
divide by 3
5a+b=-48

also 4a+2b+c=128
c=128-4a-2b=-16a-4b
12a+2b=-128
6a+b=-64
add to that -5a-b=-48
a=-16, which is reassuring, since -16t^2 is the leading coefficient in English units.
b is 32
c=128

h=-16t^2+32t+128
which is something thrown off a 128 foot high building at 32 ft/sec upward velocity.

{{{graph(300,300,-10,10,-125,150,-16x^2+32x+128)}}}