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 Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '1'; Column 2, '25' Row 3: Column 1, '2'; Column 2, '32' Row 4: Column 1, '3'; Column 2, '41' Row 5: Column 1, '4'; Column 2, '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 Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '1'; Column 2, '0 point 5' Row 3: Column 1, '2'; Column 2, '0 point 2 5' Row 4: Column 1, '3'; Column 2, '0 point 1 2 5' Row 5: Column 1, '4'; Column 2, '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 Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '1'; Column 2, 'negative 23' Row 3: Column 1, '2'; Column 2, 'negative 26' Row 4: Column 1, '3'; Column 2, 'negative 29' Row 5: Column 1, '4'; Column 2, '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

Answer 1

Dataset A.

Reason: Its first differences are 7, 9, 11, so the second differences are constant (2). Constant second differences mean the data come from a quadratic. In fact the quadratic is y = x^2 + 4x + 20.