Question

Which dataset represents a quadratic function?(1 point)
Responses

Dataset A

This table displays a set of ordered pairs (x, y), showing the relationship between x and y values.
x y
1
25
2
32
3
41
4
52
Dataset A This table displays a set of ordered pairs (x, y), showing the relationship between x and y values. x y 1 25 2 32 3 41 4 52

Dataset B

This table displays a set of ordered pairs (x, y), showing the relationship between x and y values.
x y
1
0.5
2
0.25
3
0.125
4
0.0625
Dataset B This table displays a set of ordered pairs (x, y), showing the relationship between x and y values. x y 1 0 point 5 2 0 point 2 5 3 0 point 1 2 5 4 0 point 0 6 2 5

Dataset C

This table displays a set of ordered pairs (x, y), showing the relationship between x and y values.
x y
1
−23
2
−26
3
−29
4
−32
Dataset C This table displays a set of ordered pairs (x, y), showing the relationship between x and y values. x y 1 negative 23 2 negative 26 3 negative 29 4 negative 32

Dataset D

This table displays a set of ordered pairs (x, y), showing the relationship between x and y values.
x y
1
4
2
16
3
64
4
256
Dataset D This table displays a set of ordered pairs (x, y), showing the relationship between x and y values. x y 1 4 2 16 3 64 4 256
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Answer 1

To determine which dataset represents a quadratic function, we can inspect the patterns of changes in the y-values relative to the x-values. A quadratic function has a specific structure in its outputs where the second differences of the y-values are constant.

Let's examine each dataset more closely:

### Dataset A
| x | y |
|---|----|
| 1 | 25 |
| 2 | 32 |
| 3 | 41 |
| 4 | 52 |

First differences:
32 - 25 = 7
41 - 32 = 9
52 - 41 = 11

Second differences:
9 - 7 = 2
11 - 9 = 2

**Second differences are constant. Possible quadratic function.**

### Dataset B
| x | y |
|---|-------|
| 1 | 0.5 |
| 2 | 0.25 |
| 3 | 0.125 |
| 4 | 0.0625|

First differences:
0.25 - 0.5 = -0.25
0.125 - 0.25 = -0.125
0.0625 - 0.125 = -0.0625

The differences become increasingly smaller and do not show a constant second difference. **Not a quadratic function.**

### Dataset C
| x | y |
|---|------|
| 1 | -23 |
| 2 | -26 |
| 3 | -29 |
| 4 | -32 |

First differences:
-26 - (-23) = -3
-29 - (-26) = -3
-32 - (-29) = -3

Second differences:
-3 - (-3) = 0

**Constant first differences indicate a linear function, not quadratic.**

### Dataset D
| x | y |
|---|------|
| 1 | 4 |
| 2 | 16 |
| 3 | 64 |
| 4 | 256 |

First differences:
16 - 4 = 12
64 - 16 = 48
256 - 64 = 192

Second differences:
48 - 12 = 36
192 - 48 = 144

The differences are not constant. **Not a quadratic function.**

### Conclusion:
**Dataset A** is the only dataset that represents a quadratic function as evidenced by its constant second differences.