Explanation
Correct answer: D.
Choice D is correct. The data in the scatterplot roughly fall in the shape of a downward-opening parabola; therefore, the coefficient for the term must be negative. Based on the location of the data points, the -intercept of the parabola should be somewhere between and . Therefore, of the equations given, the best model is .
Desmos solution:
Note: The quadratic regression's negative a and positive b and c match choice D's equation.
Enter in Desmos:
Reviewed and rewritten by CookSAT
Why the other choices are wrong
Choice A
Choice A is incorrect. The positive coefficient of the term means that this equation defines an upward-opening parabola, whereas a parabola that fits the data in the scatterplot must open downward.
Choice B
Choice B is incorrect because it defines a parabola with a -intercept that has a negative -coordinate, whereas a parabola that fits the data in the scatterplot must have a -intercept with a positive -coordinate.
Choice C
Choice C is incorrect. The positive coefficient of the term means that this equation defines an upward-opening parabola, whereas a parabola that fits the data in the scatterplot must open downward.