# SOLUTION: x 1_2_3_4 and y 13_22_33_46. what is the equation?

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 Click here to see ALL problems on Graphs Question 279045: x 1_2_3_4 and y 13_22_33_46. what is the equation? Answer by scott8148(6628)   (Show Source): You can put this solution on YOUR website!the differences between consecutive y terms is not constant ___ 9 _ 11 _ 13 however, the difference between consecutive differences is constant (2) ___ this means a second order (squared) relation y = ax^2 + bx + c 13 = a(1^2) + b(1) + c ___ 13 = a + b + c 22 = a(2^2) + b(2) + c ___ 22 = 4a + 2b + c 33 = a(3^2) + b(3) + c ___ 33 = 9a + 3b + c subtracting 1st eqn from 2nd eqn ___ 9 = 3a + b ___ -18 = -6a - 2b subtracting 1st eqn from 3rd eqn ___ 20 = 8a + 2b adding new eqns ___ 2 = 2a ___ 1 = a substituting ___ 9 = 3(1) + b ___ 6 = b substituting ___ 13 = (1) + (6) + c ___ 6 = c y = x^2 + 6x + 6