How do you graph $y= |x - 2| + 2$ ?

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How do you graph $y= |x - 2| + 2$ ?

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Answer 1 · 2017-12-26T15:11:45

you can see that:
when $x=2$ , $y(2)=abs(2-2)+2=0+2=2$

when $x=1$ , $y(1)=abs(1-2)+2=1+2=3$
when $x=3$ , $y(3)=abs(3-2)+2=1+2=3$

when $x=0$ , $y(0)=abs(0-2)+2=2+2=4$
when $x=4$ , $y(4)=abs(4-2)+2=2+2=4$

when $x=-1$ , $y(-1)=abs(-1-2)+2=3+2=5$
when $x=5$ , $y(5)=abs(5-2)+2=3+2=5$

and so on, in general:
when $x=2-a$ , $y(2-a)=abs(cancel(2)-acancel(-2))+2=abs(-a)+2=a+2$
when $x=2+a$ , $y(2+a)=abs(cancel(2)+acancel(-2))+2=abs(+a)+2=a+2$

We see this is a linear

so the graph will have a min when $x=2$ and go linear in each side (down when $x<2$ and up when $x>2$ )

graph{abs(x-2)+2 [-10, 10, -1, 9]}

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How do you graph $y= |x - 2| + 2$ ?

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