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.
Explanation:
here the first differences of y values are as below
[tex]\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}[/tex]
now again take difference of the first difference which is called as second difference.
[tex]\begin{gathered} 10-4=6 \\ 16-10=6 \\ 22-16=6 \\ 28-22=6 \end{gathered}[/tex]
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
