Question

Explain how you know that the function represented by the data in the given table is quadratic.XV0-17123-13-313

Answer 1

Given:

Here a table of equation is given

Required:

How to know that the function represented by the data in the given table is quadratic.

Step-by-step explanation:

here the first differences of y values are as below

`\begin{gathered} -13-(-17)=-13+17=4 \\ -3-(-13)=-3+13=10 \\ 13-(-3)=13+3=16 \\ 35-13=22 \\ 63-35=28 \end{gathered}`

now again take difference of the first difference which is called as second difference.

`\begin{gathered} 10-4=6 \\ 16-10=6 \\ 22-16=6 \\ 28-22=6 \end{gathered}`

so here we can see that the second difference is same which is 6

now if second difference of any table is equal we can say that the given table is the table of quadratic equation.

Final answer:

The second differences are all 6