F(x) = x^2 reflect across the x-axis translate left 2 units a) g (x) = (-x)^2 + 2 b) g (x) = (-x)^2 - 2 c) g (x) = + 2))^2 d) g (x) = -(x + 2)^2

The correct answer is D) g(x) = -(x + 2)^2. The given formula F(x) = x^2 creates a parabola that is open at the top. To reflect this figure across the x-axis and have it open at the bottom, the y-position of the figure on the coordinate system for every x value, which is F(x) = y = x^2 has to be inverted. This is done by negating y and respectively x^2, so to reflect the figure on the x-axis the formula would now look like this: F(x) = -y = -x^2. To move any parabola two units to the left and thereby have its root be at -2, you would simply subtract -2 from every x-position of the figure in the coordinate system. For an inverted parabola like this one the value to move it on the x-axis has to be added instead and this results in the formula from answer D: g(x) = -(x+2)^2

The first option would be correct if it were one half and not one