When values of a quadratic function are listed in a table with x-values having a constant difference, the y-vlaues will have a constant (non-zero) second-difference.
Here, we can list first and second differences for the values in the given tables to identify the quadratic function.
Table 1.
1st differences: 3, 3, 3, 3
2nd differences: 0, 0, 0, 0 . . . . this is a linear function
Table 2.
1st differences: -6, -2, 2, 6
2nd differences: 4, 4, 4 . . . . this is a quadratic function
Table 3.
1st differences: 5, -8, -3, -3
2nd differences: -13, 5, 0 . . . . can be described by a 4th degree polynomial
Table 4.
1st differences: 3, 0, -3, -3
2nd differences: -3, -3, 0 . . . . can be described by a 4th degree polynomial
