SOLUTION: A ball is tossed into the air so that the height after 1, 2, and 4 seconds is as given in the following table. If the relationship between the height of the ball h and the time t i

Question 1162781: A ball is tossed into the air so that the height after 1, 2, and 4 seconds is as given in the following table. If the relationship between the height of the ball h and the time t is quadratic, then the relationship can be written as:
h=at^2+bt+c
Use the information in the table to write a system of three equations in three variables a, b, and c. Solve the system to find the exact relationship between h and t.
t h
1 144
2 128
4 0

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
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.

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