Question

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

Answer 1

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]}