Question 1143056
The directrix is vertical (x=-5); the vertex is to the right of the directrix.  So the parabola opens to the right.<br>
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>
The given information allows us to write the equation with just one simple calculation.<br>
The vertex (h,k) is (3,-2); and p is the directed distance from the directrix to the vertex -- i.e., the directed distance from -5 to 3 -- so p=8.  Then the equation is<br>
{{{x = (1/32)(y+2)^2+3}}}