Question

which equation describes the graph? y = √(x + 4)+2 y = √(x - 4)+2 y = √(x - 2)+4 y = √(x + 2)-4

Explanation:

Step1: Recall square - root function transformation rules

The parent function of a square - root function is $y = \sqrt{x}$, and its graph starts at the origin $(0,0)$. For a function of the form $y=\sqrt{x - h}+k$, the graph of the parent function $y = \sqrt{x}$ is shifted $h$ units to the right if $h>0$ and $|h|$ units to the left if $h < 0$, and $k$ units up if $k>0$ and $|k|$ units down if $k < 0$.

Step2: Analyze the starting point of the given graph

The graph of a square - root function starts at a point. If we assume the starting point of the parent function $y=\sqrt{x}$ is $(0,0)$. Looking at the graph, we can estimate that the starting point of the given graph is at $(4,2)$.
For the function $y=\sqrt{x - h}+k$, when $x = h$, $y=k$. If $h = 4$ and $k = 2$, the function is $y=\sqrt{x - 4}+2$.

Answer:

$y=\sqrt{x - 4}+2$