Question 1143057
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I will guess that you want vertex form, since that is the form that tells you the most about the parabola.<br>
The squared term is y, so the parabola opens right or left.  The vertex form of the equation is<br>
{{{x = (1/(4p))(y-k)^2+h}}}<br>
where the vertex is (h,k) and p is the directed distance from the directrix to the vertex and from the vertex to the focus.<br>
Put the given equation in that form by completing the square and solving for x.<br>
{{{y^2+4x-8y+28 = 0}}}
{{{y^2-8y = -4x-28}}}       isolate the y terms
{{{y^2-8y+16 = -4x-12}}}    complete the square in y
{{{(y-4)^2 = -4x-12}}}
{{{4x = -(y-4)^2-12}}}      isolate the x term
{{{x = (-1/4)(y-4)^2-3}}}   solve for x<br>
This is in vertex form, so the vertex is (-3,4).<br>
The coefficient (-1/4) is 1/(4p), so p is -1.  That means the focus is 1 unit to the left of the vertex and the directrix is 1 unit to the right of the vertex.<br>
ANSWERS:
equation: {{{x = (-1/4)(y-4)^2-3}}}
vertex: (-3,4)
focus: (-4,4)
directrix: x=-2
axis: y=4<br>