Final answer:
The correct quadratic regression equation for a given dataset, represented in standard form as y = ax² + bx + c, is A. y = -0.175x² + 3.786x + 121.119. This equation properly fits the standard quadratic model, unlike the incorrect options provided.
Step-by-step explanation:
The question asks about a quadratic regression equation for a given dataset. A quadratic regression is a type of polynomial regression analysis where the degree of the polynomial is 2, aimed to best fit a set of data. The correct form of a quadratic equation is y = ax² + bx + c, where a, b, and c are coefficients that describe the equation's parabolic shape. To find these coefficients, statistical software or a calculator with regression capabilities is typically used.
Given the options provided, the one that represents a proper quadratic regression equation is A. y = -0.175x² + 3.786x + 121.119. This equation follows the standard quadratic form, whereas the other options are either not quadratic or misrepresent the structure of the quadratic equation by not correctly placing the coefficients or including all necessary terms.
Option B is incorrect because it uses a coefficient as if it were an exponent, and option C has a negative b value which should not inherently invalidate it, but the correct positive value is indicated in option A. Option D is not a quadratic equation since it lacks the x² term and therefore does not represent a quadratic regression.
To summarize, a quadratic regression equation involving a parabolic best fit line for a scatterplot or dataset will always have three terms following the form ax² + bx + c. When conducting statistical analysis, such as regression, it is crucial to have the correct form of the equation to match the characteristics of the data you are analyzing.