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

Explanation:

Step1: Analyze the function

The function $y = - 2|x|$ is an absolute - value function. The general form of an absolute - value function is $y=a|x - h|+k$, where $(h,k)$ is the vertex of the graph. For $y=-2|x|$, $h = 0$ and $k = 0$, and the vertex is at the origin $(0,0)$. The coefficient $a=-2$ indicates a vertical stretch by a factor of 2 and a reflection over the $x$ - axis.

Step2: Find points on the graph

When $x = 1$, $y=-2|1|=-2$. When $x = 2$, $y=-2|2|=-4$. When $x=-1$, $y=-2|-1|=-2$. When $x=-2$, $y=-2|-2|=-4$.

Step3: Adjust the graph

Move the red points to the following coordinates: $(-2, - 4),(-1,-2),(1,-2),(2,-4)$ and keep the blue point at the origin $(0,0)$ since there is no horizontal or vertical shift for the function $y=-2|x|$.

Answer:

Move the red points to $(-2,-4),(-1, - 2),(1,-2),(2,-4)$ and keep the blue point at $(0,0)$.