Horizontal Parabola

We are used to looking at quadratic equations where "y" is the variable that is equal to the squared "x" terms. However, in a horizontal parabola the "x" is equal to the "y" term squared. Instead of going up and down, a horizontal parabola goes from side to side. When graphing a horizontal parabola, we first need to make sure the formula is in standard form and then plot accordingly.

We are used to looking at quadratic equations that are Y is equal to something squared. Okay.

But that doesn't always have to be the case. We could end up dealing with X is equal to something Y squared. And what that really does is take a parabola, which we are used to looking at as up and down, so either straight, coefficient of positive A or negative A. And what it does instead is make it a sideways problem. So you're dealing with something like this or something like this. Okay.

Trick is that this isn't actually a function. Remember that in order to have a function we have to have one Y for every X. So if you look at something like this, that's not going to hold. So this isn't a function, but that doesn't mean we can't still try to graph it.

So what we can do is in order to graph it, think about what the relating equation is for Y equals. So I have right here X is equal to Y plus 1 squared minus 3. Think about the relating graph, Y is equal to X plus 1 squared minus 3. And think about what each component does.

The minus 3 moves the graph down three. So that is taking the Y value down three. If we are dealing with the X equals, it's going to do the same thing. Instead of taking the Y down 3 it takes the X down 3. So what you're doing is making the X three units smaller. So we would take our vertex and move it back 3. Similarly to the X plus 1.

What this is going to do is move our X coordinate of our vertex back one for a vertical parabola. It's going to move the Y back one on a side-to-side parabola. By taking the Y back one what that means is making the Y one smaller or moving it down one.

We don't have any coefficients to make this any steeper or wider, so what we found out is that our vertex is back three, one, two, three and down one. Our coefficient is positive, which tells us we have in this case an upward facing parabola where our Y values are going to be getting bigger.

Here we have no coefficient which then tells us the opposite, our X coordinates are going to be getting bigger. We're dealing with negative Xs and it's going to be going this way. We're going to have something like this. Again, you could always plug in a point if you want to get a little bit more precise graph.

Here we're dealing with negative one. So I would probably end up plugging in Y equals 0 to get an extra point. But what we've done is basically graphed a horizontal parabola by finding the vertex, pretty much the exact same way as we did before but just switching our X and our Ys.

Just to note, again this is not a function. The two pieces together, we could break it up and look at either just the top or just the bottom and those are functions. But together when we're dealing with an entire sideways parabola, it's not a function.