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### Course: Get ready for Algebra 2>Unit 3

Lesson 7: Graphs of absolute value functions

# Shifting absolute value graphs

The graph of y=|x-h|+k is the graph of y=|x| shifted h units to the right and k units up. See worked examples practicing this relationship.

## Want to join the conversation?

• I broke my replay button and I still don't understand this! Why move 3 to the right and write x-3 when x+3 seems to make sense?
• If you are trying to find where the new "0" would be, when x = 3, then x-3 =0, so this would move it to the right. for x + 3, you would have to add -3 (to the left) to get 0. The point slope form shows this best when you have y - y1 = m(x-x1). In this case, a positive y1 actually would move the graph down and a negative y1 would move it up, but when we see it in point slope form y = mx + b, the b stays what it is (positive up and negative down).
• How the equation would be if we shift it only up 4?
• The answer would've been y=|x|+4
• Why would you subtract 3 if your are going to the right of the graph on the X-Axis instead of adding? So would that mean you would add if you were going the left of the X-Axis?
• Because are now 3 to right which +3, but we need it to be 0, so we subtract 3 to do that.

When we go up again are at +4 so u need add -4

y-4=︱x-3︱
y=︱x-3︱+4
• wait.. so uhh can we like simplify
y = |x - 3| + 4
to
y = |x - 3 + 4|
and then simplify that to
y= |x + 1|
• Those are not the same equation.
y = |x-3|+4 has its vertex point at (3,4)
y = |x+1| has its vertex point at (-1,0)

Hope this helps.
• Ummm... I think we use absolute value to find the distance from 0 to the number itself. Am I correct?
• Yes, you are absolutely correct. Absolute value finds the distance of a number from 0. For example, the absolute value of -3 is 3, but the absolute value of 99 is 99. Hope this helps!
• Hi! I am currently taking Algebra 1 on Khan Academy, but I feel like I missed something. Could someone please point me to where Sal first talked about absolute value?
• You should first do the Get ready for Algebra 1 course first :)
• I kind of find it confusing.
• why is it -3 and not +3
and if we shift to the left side would it be +3?
again why
• Yes if we shift it to -3 in the x axis, that's because we want to x to be equal to 0 on our x intercept, doing that however the value we put on x we obtain the value of y, can't explain very well but that makes sense and you can try by yourself on which any number and it will be always true. Don't forget that |-x| = +x
• shift to the right is positive? shift to the left is negative?
(1 vote)
• The basic absolute value equation is: y = |x|. The vertex is at (0,0).

To shift the graph to the right, the equation becomes: y = |x-a|. To shift the graph to the left, the equation becomes y = |x+a|.

Hope this helps.
• Hi! Can someone explain how 4 is not subtracted but added? Isn't the goal to get back to zero, so isn't that why you did x-3 ?
(1 vote)
• It's different. One is doing transformation on x-axis, the other is on y-axis.

It because of the form we usually write:
y = f(x)
When we do transformation on y-axis, we simply add it.
y= f(x) + a

But when we do transformation on x-axis, it is inside f(x).
y = f(x + a)

To know why shifting like 3 to the right we have x - 3, check the top-voted answer.