Question

use technology to find points and then graph the function $y = |x + 1| - 2$, following the instructions below.

done plotting points

plot at least five points that fit on the axes below. click a point to delete it.

graph with x-axis from -10 to 10 and y-axis from -10 to 10, grid lines, and origin at (0,0)

Explanation:

Step1: Identify vertex of absolute value function

The vertex of $y=|x-h|+k$ is $(h,k)$. For $y=|x+1|-2$, this is $(-1,-2)$.

Step2: Calculate left of vertex (x=-3)

Substitute $x=-3$:
$y=|-3+1|-2=|-2|-2=2-2=0$
Point: $(-3,0)$

Step3: Calculate left of vertex (x=-2)

Substitute $x=-2$:
$y=|-2+1|-2=|-1|-2=1-2=-1$
Point: $(-2,-1)$

Step4: Calculate right of vertex (x=0)

Substitute $x=0$:
$y=|0+1|-2=|1|-2=1-2=-1$
Point: $(0,-1)$

Step5: Calculate right of vertex (x=1)

Substitute $x=1$:
$y=|1+1|-2=|2|-2=2-2=0$
Point: $(1,0)$

Step6: Calculate right of vertex (x=2)

Substitute $x=2$:
$y=|2+1|-2=|3|-2=3-2=1$
Point: $(2,1)$

Answer:

Plot the points $(-3,0)$, $(-2,-1)$, $(-1,-2)$, $(0,-1)$, $(1,0)$, $(2,1)$ (or other valid points from the function) and connect them to form a V-shaped graph with vertex at $(-1,-2)$.