have a vertex at (-4,-1) with a vertical axis of symennetry. which one has a directrix of y=-4
so far i got (x+4)^2=?(y+1)
what is the ?..?!! how do i get that
Hello peekybooyouYou're right so far. You have used the fact that the parabola $\displaystyle X^2 = 4aY$ has vertex at $\displaystyle (0,0)$ and a vertical axis of symmetry. You've replaced $\displaystyle X$ by $\displaystyle (x+4)$ and $\displaystyle Y$ by $\displaystyle (y+1)$ to give a parabola whose vertex is at $\displaystyle (-4,-1)$.
Now you need to use the fact that the parabola $\displaystyle X^2 = 4aY$ has directrix $\displaystyle Y = -a$.
If in the $\displaystyle (x,y)$ coordinates, the directrix is $\displaystyle y = -4$, in the $\displaystyle (X,Y)$ coordinates it is
$\displaystyle Y = y+1 =-3$
$\displaystyle \Rightarrow a = 3$
So in $\displaystyle (X,Y)$ coordinates the equation is $\displaystyle X^2 = 12 Y$; in $\displaystyle (x,y)$ coordinates it is $\displaystyle (x+4)^2 = 12(y+1)$
Grandad