Answer:
Step-by-step explanation:
I'm going to go way out on a limb here and say that you are probably looking for the equation that goes along with that information. If not, you'll learn something anyway!
The equation that we want to fill in is this one:
[tex](y-k)^2=4p(x-h)[/tex]
where h and k are the coordinates of the vertex and p is the distance from the vertex to either the focus or the directrix (since the vertex is directly between the 2). If our vertex is at the origin (0, 0) and the focus is at (-2, 0), first and foremost we need to decide what kind of parabola this is. Remember that a parabola wraps itself around the focus. So our parabola opens to the left (that means that in the end, the equation will be negative, but we'll get there in time). Now we need to determine p, since that's the only "mystery" and everything else was given to us.
p = 2. Filling in the equation:
[tex]-(y-0)^2=4(2)(x-0)[/tex] which simplifies to
[tex]-y^2=8x[/tex] and now we solve it for x:
[tex]-\frac{1}{8}y^2=x[/tex]
