move at least one of the 9 guide points below to complete the graph of y = |x + 2|. moving the red points…

Explanation:

Step1: Analyze the absolute - value function

The parent function of an absolute - value function is $y = |x|$. The function $y=|x + 2|$ is a horizontal shift of the parent function $y = |x|$. According to the rule of function transformation, for the function $y=f(x + h)$, if $h>0$, the graph of $y = f(x)$ shifts to the left by $h$ units. Here $h = 2$, so the graph of $y=|x|$ shifts 2 units to the left.

Step2: Find key points

For the parent function $y = |x|$, key points are $(0,0),(1,1),(- 1,1)$. For the function $y=|x + 2|$, when $x=-2$, $y = 0$; when $x=-1$, $y = 1$; when $x=-3$, $y = 1$.

Answer:

The vertex of the graph of $y = |x + 2|$ is at the point $(-2,0)$. The graph has a "V - shape" with slopes of $-1$ for $x<-2$ and $1$ for $x>-2$. To complete the graph, you can move the blue point to $(-2,0)$ and adjust the red points to maintain the correct slope and shape of the absolute - value function.