What is the equation of the parabola with vertex (-1,3) and focus (1,3)? I need an explanation please.

The distance between the focus and the vertex is designated by p.

The vertex coordinates are (h,k)=(-1,3).

If a parabola opens in the positive x direction as this one does, its equation is given by

(y-k)^{2}=4p(x-h)

It is easy to see that the distance between the focus and vertex, p, is 2 because the distance from x=1 to x=-1 is 2 units.

Plug in p, h,k and solve for x.

Oh yeah, another thing in case you need it. The directrix is a vertical line in front of the vertex the same distance from the vertex as the focus.

Therefore, the directrix would be at x=-3

See, here is what a parabola actually is. All points on the parabola are the same distance from the focus as they are from the directrix.

Draw a line from the focus to anywhere on the parabola. Then, from that point draw straight to the directrix. The distances are the same.

Thank you for all of your help galactus. I have a better understanding, but in your diagram you show v as 1,3 not -1,3 was this just a typo. Also, what would I plug in for y? Thank you for your help.

Yes, duh, that should be F(1,3). A typo.

You do not plug in anything for y. The parabola lies on its side, so it is in terms of y instead

of x. When you solve for x, you have something of the form x=ay^{2}+by+c

a, b, and c will be determined when you solve for x. That is just a general form.

If my response helps, please 'rate this answer' for me. That's all I ask.:)