How do you write ##y= x^2-18x+52 into vertex form?

Vertex Form is: ##y=(x-h)^2+k##

First, because the constant 52 doesn't help us immediately in finding a perfect square we can move it to the left with our ##y## term:

##y-52=x^2-18x##

Now we find our perfect square: ##-18/2=-9; (-9)^2=81##

##y-52+81=x^2-18x+81##

Now simplify to Vertex Form: ##y+29=(x-9)^2##

##y=(x-9)^2-29##