Question 1024401
y^2+4y+3x-4=0
{{{3x=-y^2-4y+4}}}, somewhat easy because right side contains a perfect square...
{{{3x=-1(y^2+4y-4)}}}
{{{-3x=y^2+4y-4}}}
{{{-3x=y^2+4y+4-4-4}}}----completing the square using  {{{4}}}.
{{{-3x=(y+2)^2-8}}}
{{{-3x+8=(y+2)^2}}}
{{{highlight(-3(x-8/3)=(y+2)^2)}}}
OR
{{{highlight(3(x-8/3)=-1*(y+2)^2)}}}


You might want to know why I put the equation into that form, and not into "standard form".


Study this video lesson about equations of parabolas!
<a href="https://www.youtube.com/watch?v=Wworlx39KfQ">Deriving equation for a parabola if given directrix and focus and if vertex is not at Origin</a>


Recognize that YOUR parabola has horizontal symmetry axis, and opens to the LEFT.