Question 972479
A reference model for a horizontal parabola is {{{4px=y^2}}} and allowing for translations of location,  {{{4p(x-h)=(y-k)^2}}}.  These forms come from the derivation for the equation of a parabola.  The meaning of p is the distance between the vertex (for standard position) and either the focus or the directrix.


Start from the general given equation, complete the square, and put into STANDARD FORM.


{{{y^2-16y=-4x-8}}}
{{{y^2-16y+64=-4x-8+64}}}, the constant, 64 needed for completing the square for y.
{{{(y-8)^2=-4x+56}}}
{{{-(y-8)^2=4(x-14)}}}
{{{-4(x-14)=(y-8)^2}}}
-------still not exactly standard form, but <b>vertex is (14,8)</b>,  then corresponding coefficients gives {{{4p=-4}}} and then {{{p=-1}}}.

The vertex occurs as a maximum for x value so the parabola opens to the left, and therefore the focus is 1 unit to the left of the vertex.
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Focus is (13,8);
Directrix is x=15.
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