Answer:
s = -16t² +144
Step-by-step explanation:
A graphing calculator or spreadsheet can do the quadratic regression analysis for you and tell you the equation parameters.
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Without loss of generality, we can use "a" for the coefficient of t² instead of (1/2)a. Filling in the given values, we can solve for the equation parameters:
s = at² +v0·t +s0
128 = a + v0 + s0 . . . . . for t=1
80 = 4a +2v0 +s0 . . . . .for t=2
0 = 9a +3v0 +s0 . . . . . . for t=3
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Subtracting the first equation from the other two gives ...
-48 = 3a +v0 . . . . . . [eq4]
-128 = 8a +2v0
Dividing the second of these by 2, we get ...
-64 = 4a +v0 . . . . . . [eq5]
Then, subtracting [eq4] from [eq5] gives ...
-16 = a
Substituting this into [eq4], we have ...
-48 = 3(-16) +v0
-48 = -48 + v0
0 = v0
Putting the known values into the first equation, we can find s0:
128 = -16 + 0 + s0
144 = s0
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The position equation is ...
s = -16t² + 144
