Question

Which of these tables could represents quadratic function?

X. Y
-2. -8
-1. -5
0. -2
1. 1
2. 4


X. Y
-2. 8
0. 2
2. 0
4. 2
6. 8


X. Y
1. -1
2. 4
0. -4
-1. -7
-2. -10


X. Y
1. 1
2. 4
0. 4
-1. -7
-2 -10

Answer 1

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

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The appropriate choice is Table 2.