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# Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations.$y = x^2 - 4x + 5$

## $y=x^{2}-4 x+5=\left(x^{2}-4 x+4\right)+1=(x-2)^{2}+1:$ Start with the graph of $y=x^{2},$ shift 2 units to the right, and then shift upward 1 unit.

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##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

our goal is to graft dysfunction, but we want to do it by thinking about the parent function, which is y equals X squared and what kinds of transformations would have taken place. So we need to change how this function looks before we can figure that out. So what I'm going to do is complete this square and I have y equals X squared minus four X plus four. That's a perfect try. No meal square plus one. So I just broke up the plus five into plus Foreign plus one. Now we can write the perfect try no meal square as X minus two quantity squared. So looking at this graph, this would be the original function y equals X squared, shifted to the right one, rescued me right to and shifted up one. Okay, so let's take a look at the regular graph of y equals X squared. Just it's for Texas 00 problem opening up. So now if we shift that to the right to and up one, we get something like this

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##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp