SAT Mathematics Practice Test 6

Question : 50 of 58

Marks: +1, -0

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?

$y=1.674x^2+19.76x-745.73$
$y=-1.674x^2-1.976x-745.73$
$y=1.674x^2+19.76x+745.73$
$y=-1.674x^2+19.76x+745.73$

Validate

Solution:

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 intercept 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.

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