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) = ( - (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