Precalc
posted by Matt on .
how do I graph this function?
x^2xy+2x1=0

x ^ 2  x y + 2 x  1 = 0 Add xy to both sides
x ^ 2  x y + 2 x  1 + x y = 0 + x y
x ^ 2 + 2 x  1 = x y
Roots :
When y = 0 then :
x ^ 2 + 2 x  1 = x * 0
x ^ 2 + 2 x  1 = 0 Add 2 to both sides
x ^ 2 + 2 x  1 + 2 = 0 + 2
x ^ 2 + 2 x + 1 = 2
________________________________________
Remark :
x ^ 2 + 2 x + 1 = ( x + 1 ) ^ 2
________________________________________
( x + 1 ) ^ 2 = 2 Take the square root of both sides
x + 1 = + OR  sqrt ( 2 ) Subtract 1 to both sides
x + 1  1 = + OR  sqrt ( 2 )  1
x = + OR  sqrt ( 2 )  1
x1 = sqrt ( 2 )  1 = approx 0.41
x2 =  sqrt ( 2 )  1 = approx.  2.41
Revrite x ^ 2 + 2 x  1 = x y
Divide both sides by x
x ^ 2 / x + 2 x / x  1 / x = x y / x
x + 2  1 / x = y
y = x  1 / x + 2
for x = 0
x  1 / x + 2 > + OR  infinity
Go on wolfram alpha dot com
When page be open in rectangle type :
plot x ^ 2  x y + 2 x  1 = 0
and click option =
You will see graph