Question 746995
{{{x ^ 2 - 4y - 4x + 24y = 36}}}


{{{x^2-4x+24y-4y=36}}}
{{{x^2-4x+20y=36}}}
{{{20y=-x^2+4x+36}}}
{{{y=-(1/20)x^2+(1/5)x+36/20}}}
{{{y=-(1/20)x^2+(1/5)x+9/5}}},  this is a parabola with a maximum.  y on one side is degree 1 and there is x^2 term meaning x to degree 2.


Use Completing of the Square to put into standard form:
{{{y=-(1/20)(x^2-4x)+9/5}}}
{{{y=-(1/20)(x^2-4+4)+9/5-(4)(-1/20)}}}-------this is the adding and subtracting of the missing square term.
{{{y=-(1/20)(x-2)^2+9/5+1/5}}}
{{{highlight(y=-(1/20)(x^2-2)+2)}}}--------Standard Form