Graphing Problem?

Question

graph y < |1/2x – 4| + 3. Label the vertex and 2 symmetric points.

Answer 1

First find the where the expression in the absolute value signs is zero:
(1/2)x - 4 = 0
(1/2)x = 4
x = 8
y = |(1/2)x - 4| + 3
y = |(1/2)8 - 4| + 3
y = |4 - 4| + 3
y = 0 + 3 = 3
That's the point (8, 3). That's the vertex.
Two symmetric can be found by choosing a value for y greater than 3, say y = 5.
y = |(1/2)x - 4| + 3
5 = |(1/2)x - 4| + 3
2 = |(1/2)x - 4|
+/- 2 = x/2 - 4
2 = x/2 - 4
6 = x/2
x = 12
-2 = x/2 - 4
2 = x/2
x = 4
That gives you the symmetric points (4, 5) and (12, 5)
Bear in mind that none of these points satisfy the inequality, but are on the border line. Points that satisfy the inequality are in the shaded area below the dashed line.

http://s236.photobucket.com/albums/ff177/jsardi56/?action=view¤t=graphinequality10-28-07.jpg