The table which represents a quadratic relationship is in option [tex]D[/tex].
What is quadratic relationship ?
A quadratic relationship is a mathematical relation between two variables that follows the form of a quadratic equation.
Quadratic sequence [tex]=an^2 +bn+c[/tex]
So, According to the definition mentioned above if table follows the form of a quadratic equation then it is in quadratic relationship.
So,
To find out quadratic relationship,
We will find first difference in every table and then second difference (Second difference is the difference between the first difference).
We have,
Table A;
[tex]\left \begin{array}{ccccc}x& \ &f(x)&First\ Difference & Second\ Difference \\-2& &4&2-4=-2\\-1& &2&1-2=-1&-1+2=1\\0& \ &1&0.5-1=-0.5&-0.5+1=0.5\\1& &0.5&0.25-0.5=-0.25&-0.25+0.5=0.25\\2& &0.25&0.125-0.25=-0.125\\3& &0.125\end{array}\right[/tex]
So, In the above table we can see that second difference is not equal that means it is not in quadratic relationship.
Now,
Let Table D;
[tex]\left \begin{array}{ccccc}x& \ &f(x)&First\ Difference & Second\ Difference \\-2& &-23.4&\\-1& &-23.2&-23.2+23.4=-0.2&0.2-0.2=0\\0& \ &-23&-23+23.2=-0.2&0.2-0.2=0\\1& &-22.8&-22.8+23=-0.2&0.2-0.2=0\\2& &-22.6&-22.6+22.8=-0.2\\3& &-22.4&-22.4+22.6=-0.2\end{array}\right[/tex]
So, here in this table, we can see that second difference is equal that means it is in quadratic relationship.
Hence, we can say that the table which represents a quadratic relationship is in option [tex]D[/tex].
To know more about quadratic relationship click here
https://brainly.com/question/17109031
#SPJ3
