How to graph an absolute value function?
- First, find its vertex.
- Second, find its x-intercepts,
- Third, connect the vertex with the x-intercepts.
Step 1
How to find the vertex?
The general form of an absolute value function:
- y = a|x - h| + k, where (h, k) is vertex and a - coefficient
Given function is:
Its vertex is (- 3, - 2), this is our first point to plot, point A.
Step 2
How to find x-intercepts?
Set y = 0 and solve for x:
- |x + 3| - 2 = 0
- |x + 3| = 2
- x + 3 = 2 and x + 3 = - 2
- x = - 1 and x = - 5
So the x-intercepts are ( - 5, 0) and (- 2, 0), points B and C.
Step 3
Connect the vertex (- 3, - 2) with points ( - 5, 0) and (- 2, 0) and here is your graph.