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Problem-Solving and Data Analysis / Two-variable data: Models and scatterplots Difficulty: Easy

The figure presents a scatterplot in the x y plane. The numbers 0 through 6, in increments of 1, are indicated on the x axis. The numbers 0 through 20, in increments of 2, are indicated on the y axis. There are 12 data points in the scatterplot. The data points are in the shape of a parabola that opens upward. The data points begin on the y axis at 20, and trend downward and to the right until they reach a first low point with coordinates 2 point 5 comma 5 and a second low point with coordinates 3 comma 5. Then the data points trend upward and to the right until they reach the last point with coordinates 5 point 5 comma 20.

Of the following, which is the best model for the data in the scatterplot?

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Explanation

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 y-intercept near $the point with coordinates 0 comma 20$ and a vertex with an approximate x-value of 2.5. Of the given choices, only choice B gives an equation of an upward-facing parabola with a y-intercept at $the point with coordinates 0 comma 20$ . Furthermore, substituting 2.5 for x into the equation in choice B yields $y equals 5$ . This is approximately the y-value of the vertex of the model.

Choices A, C, and D are incorrect. These equations don’t give a graphical model that best fits the data. At $x equals 0$ , they have y-values of $negative 20$ , $negative 3$ , and 3, respectively. At $x equals 2 point 5$ , they have y-values of $negative 35$ , $negative 3$ , and 3, respectively.