study this table.\n| x | y |\n| -3 | -2 |\n| -2 | 0 |\n| 0 | 4 |\n| 4 | 12 |\nwhich best describes the…

Explanation:

Step1: Calculate first - differences

For $x=-3,y = - 2$; for $x=-2,y = 0$. First - difference of $y$ values: $0-(-2)=2$. For $x=-2,y = 0$; for $x = 0,y = 4$. First - difference of $y$ values: $4 - 0=4$. Since the first - differences are not constant, the function is not linear.

Step2: Check for quadratic nature

A quadratic function has non - constant first - differences. Here, the first - differences are $2,4,\cdots$. We also note that for a linear function, we would have a constant first - difference. And a common ratio is for exponential functions. Since the first - differences are non - constant, it is quadratic and we have found that the first - differences start with 2.

Answer:

quadratic with a common first difference of 2