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# Graphing a Horizontal Parabola - Concept

###### Carl Horowitz

###### Carl Horowitz

**University of Michigan**

Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

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.

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###### Carl Horowitz

B.S. in Mathematics University of Michigan

He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his step-by-step explanations are easy to follow.

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