Question 363181: How do you graph absolute value functions?
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website! y = 2|3x + 6| - 4
Finding the vertex:
1. Set what's between the absolute value bars = 0
3x + 6 = 0
3x = -6
x = -2
That's the x-coordinate of the vertex.
2. Substitute that in the equation to find the y-coordinate
of the vertex:
y = 2|3(-2)+6| - 4
y = 2|-6+6| - 4
y = 2(0) - 4
y = -4
(Shortcut for this step: the y-coordinate of the vertex is
just the number that's added to the absolute value term, in this
case -4, because when you substitute the x-coordinate the
absolute value term will always be 0)
3. The vertex is (-2,-4)
Plot that:
4. Find one other point, say the y-intercept, so let x=0,
y = 2|3(0) + 6| - 4
y = 2|0 + 6| - 4
y = 2|6| - 4
y = 2(6) - 4
y = 12 - 4
y = 8
5. Plot the y-intercept (0,8)
6. Draw a line through that point stopping at the vertex (-2,-4)
7. draw another line to make a symmetrical V-shaped graph, with vertex (-2,-4):
That's it!
Edwin
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