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CCSS.Math:

we're told the graph of the function f of X is equal to x squared we see it right over here in gray is shown in the grid below graph the function G of X is equal to X minus 2 squared minus 4 in the interactive graph and this is from the shifting functions exercise on Khan Academy and we can see we can change we can change the we can change the graph of G of X but let's see we want to graph it properly so let's see how they relate well let's think about a few things let's first just make G of X completely overlap well actually that's completely easier said than okay there you go now they're completely overlapping and let's see how they're different well G of X if you look at what's going on here instead of having an x squared we have an X minus 2 squared so one way to think about it is when x is 0 you have 0 squared is equal to 0 but how do you get 0 here well X has got to be equal to 2 2 minus 2 squared is 0 squared if we don't look at the negative 4 just yet and so we would want to shift this graph over 2 to the right this is essentially how much do we shift to the right it's sometimes a little bit counterintuitive that we have a negative there because you might say well negative that makes me think that I want to shift to the left but you don't have to remind yourself is like well okay for the original graph when it was just x squared to get to get the 0 squared I just have to put x equals 0 now to get a 0 squared I have to put in a 2 so this is actually shifting the graph to the right and so what do we do with this negative 4 well this is a little bit more intuitive or at least for me when I first learned it this literally will just shift the graph down whatever your value is of X minus 2 squared it's going to shift it down by 4 so what we want to do is just shift both of these points down by 4 so this is going to go from 9 this is going to go from the coordinate 5 comma 9 to 5 comma 4 go down for 5 comma 5 and it's going to go from 2 comma 0 to 2 comma negative 4 2 comma negative 4 did I do that right I think that is I think that's right what essentially what we have going on is G of X is f of X shifted to to the right and four down two to the right and four down and notice if you look at the vertex here we shifted two to the right and four down and I and I shifted this one also this one also I shifted two to the right and four down and there you have it we have we have we have graphed G of X which is a shifted version of f of X