Which is the standard form of the equation of the parabola that has a vertex of (–4, –6) and a directrix of y = 3?
+128407 The directrix is above the vertex, so this parabola turns downward
The form is
-4p [ y - k ] = [x - h]^2
(h, k) is the vertex = (-4, -6 )
And p is the distance between the vertex and the directrix given by 3 - k = 3 - (-6) = 9
So we have
-4(9) [ y - (-6) ] = [ x - (-4) ] ^2
-36 [ y + 6] = [ x + 4 ] ^2 divide both sides by -36
y + 6 = -(1/36) (x + 4)^2
y = -(1/36) ( x + 4)^2 - 6
