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I have posted a link there to this topic so the OP can see my work.Find the range of (x^2-6x+9)/(2x-8).?

Hello. I was given this in an assignment recently. When my teacher handed out the answer sheet after he had marked the assignments. I was puzzled to find that he had found the range using the discriminant of the quadratic formula. I will denote Lambda as Y since i don't have a lambda button. Here is the working:

Y=(x^2-6x+9)/(2x-8)

Y(2x-8)=(x^2-6x+9)

X^2+(-2Y-6)x+9+8Y=0

(-2Y-6)^2-4(9+8Y) ≥0

and then through working eventually arrived at:

Y≤ 0 or Y ≥ 2.

I really don't get how he used this to find the range or how he got ≤ and ≥ in the final result. Please help I have a test coming up soon and this is the only thing I don't understand.