To determine which tables represent quadratic relationships, we need to look for a pattern in the values of \( y \) that suggests a quadratic function. A quadratic relationship will display a constant second difference in the \( y \) values when the \( x \) values are incremented.
Let's find the differences for each table:
Table 1:
- \( y \): 1, 2, 4, 8
- First differences: 1, 2, 4 (2-1, 4-2, 8-4)
- Second differences: 1, 2 (2-1, 4-2)
Not constant, so not quadratic.
Table 2:
- \( y \): -2, -4, -8, -16
- First differences: -2, -4, -8 (-4 - (-2), -8 - (-4), -16 - (-8))
- Second differences: -2, -4 (-4 - (-2), -8 - (-4))
Not constant, so not quadratic.
Table 3:
- \( y \): -2, 0, 2, 4
- First differences: 2, 2, 2 (0 - (-2), 2 - 0, 4 - 2)
- Second differences: 0, 0 (2 - 2, 2 - 2)
Second differences are constant, so this is quadratic.
Table 4:
- \( y \): 3, 4, 5, 6
- First differences: 1, 1, 1 (4 - 3, 5 - 4, 6 - 5)
- Second differences: 0, 0 (1 - 1, 1 - 1)
Second differences are constant, but it represents a linear relationship.
Table 5:
- \( y \): -4, -8, -10, -10
- First differences: -4, -2, 0 (-8 - (-4), -10 - (-8), -10 - (-10))
- Second differences: 2, 2 (0 - (-2), -2 - (-4))
Second differences are constant, so this is quadratic.
Table 6:
- \( y \): 4, -4, -4, 4
- First differences: -8, 0, 8 (-4 - 4, -4 - (-4), 4 - (-4))
- Second differences: 8, 8 (0 - (-8), 8 - 0)
Second differences are constant, so this is quadratic.
In summary, the tables representing quadratic relationships are:
- Table 3
- Table 5
- Table 6
1 answer