Question

find the equation at^2+bt+c

given t=0,1,2

(0,6) (1,75) (2,112)

Answer 1

theres a matrix setup which makes this go pretty easily

Answer 2

rref{{0,0,1,6},{1,1,1,75},{2^2,2,1,112}}

http://www.wolframalpha.com/input/?i=rref%7B%7B0%2C0%2C1%2C6%7D%2C%7B1%2C1%2C1%2C75%7D%2C%7B2%5E2%2C2%2C1%2C112%7D%7D

Answer 3

usng the rightmost column as the values for a b and c, we get

http://www.wolframalpha.com/input/?i=-16n%5E2%2B85n%2B6

Answer 4

of course, there are more laborious, by hand, methods .... if need be