Question

question 13 (4 points) determine if the model of best fit is linear or quadratic, explain your reasoning. to receive credit, you must state how you know algebraically. x | 2 | 3 | 4 | 5 | 6 y | 6 | 0 | -2 | 0 | 6

Explanation:

Step1: Calculate first differences of $y$

First differences: $0-6=-6$, $-2-0=-2$, $0-(-2)=2$, $6-0=6$

Step2: Calculate second differences

Second differences: $-2-(-6)=4$, $2-(-2)=4$, $6-2=4$

Step3: Identify model type

Since second differences are constant, the model is quadratic.

Answer:

The model of best fit is quadratic, because the second differences of the $y$-values are constant (all equal to 4), which is the defining characteristic of a quadratic relationship.