On the graph, plot all relevant points for y=x^2-4x+y^2-2y+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.

Question

On the graph, plot all relevant points for y=x^2-4x+y^2-2y+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!!

Reiny · Answer

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
(x-2)^2 + (y-3/2)^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
(x-2-2)^2 + (y-3/2+1)^2 = 1/4
(x-4)^2 + (y-1/2)^2 = 1/4

expand it if you will
new centre is (4,1/2), radius is still 1/2

jenny · Answer

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=;)