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Current time:0:00Total duration:6:12

CCSS.Math:

this right over here is the graph of y is equal to absolute value of x which you might be familiar with if you take X is equal to negative 2 the absolute value of that is going to be 2 negative 1 absolute value is 1 0 absolute value is 0 1 absolute value is 1 so on and so forth what I want to do in this video is think about how the equation will change if we were to shift this graph so in particular we're going to first think about what would be the equation of this graph if we shift if we shift 3 to the right and then think about how that will change if not only do we shift 3 to the right but we also shift 4 up shift 4 up and so once again pause this video like we always say and figure out what would the equation be if you shift 3 to the right and 4 up alright now let's do this together so let's just first shift 3 to the right and think about how that might change the equation so let's just visualize what we're even talking about so if we're going to shift 3 to the right it would look like it would look like this so that's what we first want to figure out the equation for and so how would we think about it well one way to think about it is well something interesting is happening right over here at x equals 3 before that interesting thing was happening at x equals 0 now it's happening at x equals 3 and the interesting thing that happens here is that you switch signs inside the absolute value you're instead of taking an absolute value of a negative you're now taking the absolute value as you cross this point of a positive and that's why we see a switch in direction here of this line and so you see the same thing happening right over here so this point right over here we know that our function we know that our equation needs to evaluate out to 0 and this is where it's going to switch switch signs and so say okay well this looks like an absolute value so it's going to have the form Y is equal to the absolute value of something and so you say okay how do I if X is 3 how do I make that equal to 0 well I can subtract 3 from it if I say Y is equal to the absolute value of X minus 3 well let's try it out let's see if it makes sense so when X is equal to 3 3 minus 3 is 0 absolute value that is 0 that works out when X is equal to 4 4 minus 3 is 1 absolute value of 1 is indeed is indeed 1 and if X is equal to 2 well 2 minus 3 is negative 1 but the absolute value of that is 1 so once again I'm showing you this by really trying out numbers trying to give you a little bit of intuition because that wasn't obvious to me when I first learned this that if I'm shifting to the right which it looks like I'm increasing in X value but what I would really do is replace my X with an X minus the amount that I'm shifting to the right but I encourage you to try numbers and think about what's happening here at be at this vertex right over here what whatever was in the absolute value sign was equaling 0 it's when whatever was in the absolute value side is switching from negative signs to positive signs so once again if you switch if you shift 3 to the right that happens that has to happen at x equals 3 so whatever is inside the absolute value sign has to be equal to 0 at x equals 3 and this you know pause this video and really think about this if it isn't making sense and even as you get more and more familiar with this encourage you to try out the numbers that will give you more instead of just memorizing if I shift to the right I replace X with X minus the amount that I shift always try out the numbers and try to get an intuition for that why that works but now let's start from here and shift 4 up and shifting 4 up is in some ways a lot more intuitive so let me do that let me shift for up alright let me move I'm going to go up one two three and four I think I got that right so now I've shifted four up and this is a reminder of what we've even done the first part we shifted three to the right and now we are shifting four up so now now we are shifting four up so before y equals zero here but now Y needs to be equal to four so whatever this was evaluating do we I now have to add forward to it so when we just shifted three to the right our equation was y is equal to the absolute value of X minus three but now whatever we were getting before we now have to add 4 to it we're going up in the vertical direction so we just have to add four now this makes a little bit more sense if you're shifting in the vertical direction if you shift up in the vertical direction well you just add a constant by the amount you're shifting if you shift down in the vertical direction well you would subtract if we said shift down four you would subtract four right over here the less intuitive thing is what we did with X is when you shift to the right you actually replace your X with X minus the amount that you shifted but once again tryout numbers until it really makes some intuitive sense for you but this is what we would finally get the equation of this thing right over here is y is equal to the absolute value of x minus three plus four