Question 1152038
what is the vertex, focus, and equation of directrix


The standard form is {{{(x - h)^2 = 4p (y - k)}}}, where the focus is ({{{h}}},{{{ k + p}}}) and the directrix is {{{y = k - p}}}. 

If the parabola is rotated so that its vertex is ({{{h}}},{{{k}}}) and its axis of symmetry is parallel to the {{{x}}}-axis, it has an equation of {{{(y - k)^2 = 4p (x - h)}}}, where the focus is ({{{h + p}}},{{{ k}}}) and the directrix is{{{ x = h - p}}}

{{{(y+3)^2 = -4(x-2)}}}......here you have an equation of rotated parabola in vertex form

so,
{{{h=2}}}, {{{k=-3}}}, {{{4p=-4}}}=>{{{p=-1}}} 

= >vertex is at  ({{{2}}},{{{-3}}})

=> focus is at ({{{h + p}}},{{{ k}}}) =({{{2 -1}}},{{{ -3}}}) = ({{{1}}},{{{-3}}})

=>  equation of directrix is {{{ x = h - p}}}=>{{{ x = 2 - (-1)}}}=>{{{ x = 2+1}}}=>{{{ x = 3}}}



 {{{drawing( 600, 600, -10, 10, -10, 10,
circle(2,-3,.12), locate(2,-3,V(2,-3)),
circle(1,-3,.12), locate(1,-2.5,F(1,-3)),blue(line(3,10,3,-10)),
 graph( 600, 600, -10, 10, -10, 10,-sqrt(-4(x-2))-3, sqrt(-4(x-2))-3)) }}}