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## Homework Statement

A curve has equation (x^2 - 2x + 2)/(x^2 + 3x + 9). I need to prove that the range of values of y for this curv eis 2/27 =< y =< 2

I know how it should be worked but I can't understand why it's done that way.

My teacher simply arranged the equation in the form (x^2 + 3x + 9)y = x^2 - 2x + 2 which leads to the equation (y-1)x^2 + (3y+2)x + 9y - 2 = 0 and then said "For range, b^2 - 4ac >= 0"

This is what I'm having trouble understanding. What does the range have to do with b^2 - 4ac >= 0. I want to know the reasoning behind this

I'd appreciate any answers :)

Thanks