SM2 14.2-2: Graphing a Horizontal Parabola

Added: 2026-05-10

[00:00:00]Hello and welcome. So for the video  today we're going to be graphing a parabola. Specifically we're going  to be graphing a horizontal parabola, right? For anything for parabolas the first  thing you've got to know is you have to know for sure what direction you're looking at, right?  And how you can tell that is by looking at your equation. So for here we have y plus 2 squared.  Now where that square is tells you exactly what direction you're going. For this one you're either  going to the left or you are going to the right.

[00:00:33]Now how do we know which one is that, right? Left  or right. And how we can tell is by looking at our number where we can find the focal diameter,  and that's going to be negative 4. All right, well think about it. If you're going left or  right, which direction is a negative number?

[00:00:50]Left. Right, which means this is our case. We're  going to be going left for our parabola for this one. Okay. So when we're looking at that one then  I'd say all right, going left. And then we'll be using our general equation for parabolas. So that  would be y minus k squared equals 4p, x minus h. Oh not plus, minus k. All right, and this is  your general equation for a horizontal parabola.

[00:01:18]But let me just keep it running from there. And  we'd say, all right, now that we're going to the left.

[00:01:23]What we need to know now is we need to know the  p-value. And so our number is negative 4. So that means 4p equals negative 4. How would you solve  for the p-value? Well that's dividing by 4 both sides and then p equals negative 1. And this is  going to be where a lot of the work comes from is because once we know we're going horizontally,  specifically to the left, we know the focus is within the direction of opening and we know the  directrix is behind the parabola. And what's cool about knowing the p-value is that we know that  that value is going to be a p value to the focus, a p value to the directrix, and we  know the next points on the parabola will be a 2p distance from the focus both ways. Okay,  so we can essentially just find it. So once we know our vertex, well our vertex is just h comma  k, where h and k can be seen from those original shifts with the x and the y. Notice that it's  subtraction here so we're going to be using the opposite operation of what we see. So with the  x because all coordinate points are x comma y, right? So then you'd say all right,  so negative 3, what's the opposite of negatives? That's a positive, right? Same thing  with the inverse of addition, subtraction. Okay, so your vertex is at 3, negative 2. So 3, negative 2, point right here is your vertex.

[00:02:47]Okay, in order to find the focus we're now  going to go p distance to the left. Now our p is negative 1 but if we're talking about a  distance, right, that's just a distance of 1.

[00:02:58]Distances can't be negative. So we know  we're going 1 to the left. Bam. Focus.

[00:03:03]Same thing we know if we're going  1 to the left then 1 to the right will be your directrix. Okay, so now we know all  that lovely information. So focus is going to have to be at 2 comma negative 2. And the directrix  has to be, because it's crossing the x-axis at 4, it's x equals 4 as your line for this one. Okay,  now if you want to look at the formulaic way to find this because it's going horizontal we'll be  adding your p-value to h and then comma k. And this will be x equals your h value but subtract  p. And those are the formulaic ways. So if you take your vertex value which is 3 plus p which  is negative 1 comma negative 2 we'll get the same thing because what's 3 plus a negative 1? That's  the same thing as 3 minus 1. That's 2, right? So you could go the formulaic approach or if you know  like your straight definitions and relationships that's a, in my opinion, a little faster way to  go for these ones. Okay, and now all we got to do is point the uh like grab the other point on  our parabola which we know that from our focus is a straight 2p distance up or down. Well if our  p distance is a 1 that means we're going up 2.

[00:04:21]There's your other point. And down 2. There's your  other point. Oops as I go down three. Down two.

[00:04:27]Okay. And it's always from your focus  because we know the parabola has to go up, right? It can't mystically do like a straight  line. So we have that nice curve in there. Okay. So make sure when you're using your graphing tool, so  make sure you're using the right one. This is your horizontal parabola. It will force you to graph  your vertex first then you can graph either this top point or the bottom point. As long as you  grab either one we'll graph that one correctly.

[00:04:54]Okay, now specifically the only thing it wants  on that graph is it wants the parabola itself.

[00:05:00]All right, it says graph the parabola. That's  this thing. Okay, does it want either any of those three dots on there? No it doesn't.  Okay, it just wants the parabola itself.

[00:05:10]The little red dots for placers aren't actually  dots on the graph. Okay, they're not gonna, you don't need the dot tool on top of them. Just  use the red tools or just the red dots are just placers for the actual shape so don't worry about  those too much. Then you have the focus which that point right there, actually put a dot for it and  then you have the directrix which is this line.

[00:05:34]The line you're going to be graphing isn't dotted.  That's okay. Don't freak out. Okay, and that is it. That's graphing a horizontal parabola. That's  all the information you need. Thanks for watching.