Final answer:
To rank the functions f(x) = x² + 6x - 1, g(x) = -x² + 2, and h(x) = 2x² - 4x + 3 based on their axis of symmetry, the functions are ranked from least to greatest as h(x), g(x), f(x).
Step-by-step explanation:
To rank the functions f(x) = x² + 6x - 1, g(x) = -x² + 2, and h(x) = 2x² - 4x + 3 based on their axis of symmetry, we need to find the axis of symmetry for each function. The axis of symmetry for a quadratic function in the form ax² + bx + c is given by x = -b/2a. Calculating the axis of symmetry for each function gives: For f(x): x = -6/2 = -3, For g(x): x = 0/(-2) = 0, For h(x): x = 4/(2*2) = 1. Based on the values of the axis of symmetry, we can rank the functions from least to greatest as B) h(x), g(x), f(x).