Final answer:
The correct quadratic model for the given set of values is Option A: y= -3x^2 + 6x - 2, as it perfectly matches all the provided points when the x-values are substituted into the equation.
Step-by-step explanation:
To find a quadratic model for the given set of values (-1,-11), (0,-2), (1,1), we need to check which of the given options correctly corresponds to these points.
- We start by substituting x = -1, x = 0, and x = 1 into each equation to see if the y-values match the ones given.
- For option A, substituting yields: y = -3(-1)^2 + 6(-1) - 2 = -3 - 6 - 2 = -11, which matches the first point. When x = 0, y = -2, and for x = 1, y = 1. So, all points match for option A.
- Options B, C, and D will not match all the given points when we substitute the x-values.
Therefore, the correct quadratic model is Option A: y= -3x^2 + 6x - 2.