How to find vertex, focus and directrix of a horizontal parabola in standard form

Learn how to graph a horizontal parabola. A parabola is the shape of the graph of a quadratic equation. A parabola is said to be horizontal if it opens to the left or opens to the right. A horizontal parabola results from a quadratic equation in which the y part of the equation is squared.

To sketch the graph of a parabola, we first identify the vertex, the focus and the directrix. To do this, we first write the equation in the form (y - k)^2 = 4p(x - h), where (h, k) is the vertex and p is the distance between the vertex and the focus.

After expressing the equation in the form (y - k)^2 = 4p(x - h), the vertex is given by (h, k), the focus is given by (h + p, k) and the directrix is given by the line x = h - p. After obtaining the vertex, the focus and the directrix, we can then sketch the parabola.
#conicsections #parabolaconicsections

[arcos]

I passed my math class this semester... I cant thank you enough for all your help and wisdom.
Chico State boiiii!!!

[rav]

Could you put a minute of dead space at the end of the video after your done speaking because youtube has preview boxes that cover the board. So, I missed the tail end of that.

[Duxa_]

Thanks! Do you have a video of finding focus, vertex and directrix without completing the square? For example y=3x^2-6x+1 (without completing the square) ?

More specifically why we use things that we use to figure it out. Like why all of a suddent its a = 1/4p for P

[YoshiclueAJ]

I noticed that the standard equation is different?? In another video you said it was (x-h)^2=4p(y-k) and in this one it's (y-k)^2=4p(x-h). Why is that?? How do I know which one to use?

[makaiokalahama]

I wish I could have this teacher for pre-calc; mine is terrible :(

[timeechos]

Question, how would you find the directrix, focus, and p for y = 1/8(x=3)^2 + 2? and x = 1/16(y-3)^2 + 1. I use equations y = 1/4p (x-h)^2 + k and x = 1/4p (y-k)^2 + h

[LuvKayv]

it was very horrible I got it all wrong