Answer:
The table is a quadratic function
Step-by-step explanation:
Given
The attached table
Required
Tell if it is a quadratic function
The difference in the x values are uniform (i.e. difference of 1), so the following method can be applied.
(1) Subtract adjacent y values.
![d_1=2 - 16 = -14](https://tex.z-dn.net/?f=d_1%3D2%20-%2016%20%3D%20-14)
![d_2=-2 - 2 = -4](https://tex.z-dn.net/?f=d_2%3D-2%20-%202%20%3D%20-4)
![d_3 = 4--2 = 6](https://tex.z-dn.net/?f=d_3%20%3D%204--2%20%3D%206)
![d_4 = 20 - 4 = 16](https://tex.z-dn.net/?f=d_4%20%3D%2020%20-%204%20%3D%2016)
(2) Subtract adjacent differences in (1) above
![d_5 = d_2 - d_1 = -4 --14 = 10](https://tex.z-dn.net/?f=d_5%20%3D%20d_2%20-%20d_1%20%3D%20-4%20--14%20%3D%2010)
![d_6 = d_3 - d_2 = 6 --4 = 10](https://tex.z-dn.net/?f=d_6%20%3D%20d_3%20-%20d_2%20%3D%206%20--4%20%3D%2010)
![d_7 = d_4 - d_3 = 16 -6 = 10](https://tex.z-dn.net/?f=d_7%20%3D%20d_4%20-%20d_3%20%3D%2016%20-6%20%3D%2010)
Notice the calculated differences in (2) are the same.
<em>Hence, the table is a quadratic function</em>