Explanation
Correct answer: B.
Choice B is correct. The graphical model that most closely fits the data in the scatterplot is a model in which the number of data points above and below the model are approximately balanced. Fitting a graphical model to the data shown results in an upward-facing parabola with a -intercept near and a vertex with an approximate -value of . Of the given choices, only choice B gives an equation of an upward-facing parabola with a -intercept at . Furthermore, substituting for into the equation in choice B yields . This is approximately the -value of the vertex of the model.
Desmos solution:
Enter in Desmos:
Reviewed and rewritten by CookSAT
Why the other choices are wrong
Choice A
Choice A is incorrect. These equations don't give a graphical model that best fits the data. At , they have -values of , , and , respectively. At , they have -values of , , and , respectively.
Choice C
Choice C is incorrect. These equations don't give a graphical model that best fits the data. At , they have -values of , , and , respectively. At , they have -values of , , and , respectively.
Choice D
Choice D is incorrect. These equations don't give a graphical model that best fits the data. At , they have -values of , , and , respectively. At , they have -values of , , and , respectively.