The scatterplot below shows the amount of electric energy generated, in millions of megawatt-hours, by nuclear sources over a 10‑year period.

Of the following equations, which best models the data in the scatterplot?

Options

A. `y=1.674x^2+19.76x-745.73`
B. `y=-1.674x^2 - 19.76x-745.73`
C. `y=1.674x^2 + 19.76x+745.73`
D. `y=-1.674x^2 + 19.76x+745.73`

Answer

D

Explanation

The data in the scatterplot roughly fall in the shape of a downward-opening parabola, therefore, the coefficient for the `x^2` term must be negative. Based on the location of the data points, the y-intercept of the parabola should be somewhere between 740 and 760. Therefore, of the equations given, the best model is` y = −1.674x^2 + 19.76x + 745.73`.
Choices A and C are incorrect. The positive coefficient of the `x^2` term means that these these equations each define upward-opening parabolas, whereas a parabola that fits the data in the scatterplot must open downward. Choice B is incorrect because it defines a parabola with a yintercept that has a negative y-coordinate, whereas a parabola that fits the data in the scatterplot must have a y-intercept with a positive y-coordinate.