college algebra
posted by jenny on .
On the graph, plot all relevant points for y=x^24x+y^22y+8. Then give the equation for a graph that shifts down 1 unit and to the right 2 units. If it is a function, give its domain and range.
Thank you!!

I find it odd that your textbook stated the equation in this unsimplified form, since we could combine the two y terms to read
x^2  4x + y^2  3y + 8 = 0
From that form I recognize a circle.
let's complete the square:
x^2  4x + 4 + y^2  3y + 9/4 = 8+4+9/4
(x2)^2 + (y3/2)^2 = 1/4
so centre is (2,3/2) and radius is 1/2
we want to move this 1 unit down and 2 to the right, so
(x22)^2 + (y3/2+1)^2 = 1/4
(x4)^2 + (y1/2)^2 = 1/4
expand it if you will
new centre is (4,1/2), radius is still 1/2 
It was on a test. I think it was written like that to trick us. Normally I don't have a problem with math, but this teacher is pretty tricky! I really appreciate all of your help=;)