Which type of function best models the data in the table? Justify your choice.

Answer: Quadratic equation:  [tex]y=-2x^2+32x+22[/tex]Explanation: We need to find best model of given data in the table. 1) Linear: For linear slope of the line must be same. Slope is change in y over change x must be same. But if we find change in y over change x for this table. They won't be same. This table value can't be linear. [tex]\frac{142-118}{6-4}\neq \frac{150-142}{8-6} [/tex]2) Quadratic: For quadratic equation. we will take standard form of quadratic equation [tex]y=ax^2+bx+c[/tex]. Using any three value of table we will find a, b and c and then we satisfy other value of of table. [tex]y=ax^2+bx+c[/tex]Point 1: (4,118) [tex]\Rightarrow 118=16a+4b+c[/tex]Point 2: (6,142) [tex]\Rightarrow 142=36a+6b+c[/tex]Point 3: (8,150) [tex]\Rightarrow 150=64a+8b+c[/tex]Now we have three equation and to solve for a, b and c. Using elimination method we get the value of a=-2, b=32 and c=22. So, Quadratic equation [tex]y=-2x^2+32x+22[/tex]So, we get quadratic model for the given data in the table.