# How do you graph y=sqrtx-2 and compare it to the parent graph?

$y = \sqrt{x} - 2$ is graphed by shifting the graph of $y = \sqrt{x}$ down two. $y = \sqrt{x}$ is basically half of a sideways parabola opening to the right for positive y-values. $y = \sqrt{x}$ implies $y = + \sqrt{x}$, where y equals the positive square root of x, so inputting a value such as 9 for x yields 3 (as opposed to $y = \pm \sqrt{x}$ which, for 9, yields 3 and -3). Additionally, x cannot be a negative value, so the graph for $y = \sqrt{x}$ starts at the origin ($y = \sqrt{0} = 0$) and curves up and to the right in the first quadrant. $y = \sqrt{x} - 2$ is a transformation of $y = \sqrt{x}$ two units down (as $y = x - 2$ is a transformation of $y = x$ two units down). Thus, the graph of $y = \sqrt{x} - 2$ is: