Question

Convert this equation so that it could be entered into a calculator in the standard y= format. x^2 - 4xy + 4y^2 - 8y + 2 = 0

Answer 1

First off, you can see that it's 2nd-degree in both x and y, so there is no simple y=f(x) expression. It's the equation of a rotated parabola, so there will be a top branch and a bottom branch.

Anyway, express it as a quadratic in y:

x^2 - 4xy + 4y^2 - 8y + 2 = 0
4y^2 - (4x+8)y + (x^2+2) = 0
Using the quadratic formula,

y = [(4x+8)±√((4x+8)^2 - 4(4)(x^2+2))]/8
= [x+2±√(4x+2)]/2

so, you can see there are two branches to the function.