Hey there. Um, in this video I'm going to
talk to you, um, uh, just a brief introduction of
um, or to the quadratic formula.
Uh, this is
going to, um, I think you're gonna enjoy the
quadratic formula. Um, because it's going to
help you out and maybe save some time, ah, when
we're trying to solve quadratics. Um, the
first thing I want to do is I want to
talk to you about, um, um, what we kind of
already know,
what we learned in, in the
previous sections in this, in this module.
Um, you know, one important, um, thing we saw in
what some of the first problems we did
in, in the first section, is we maybe solve
problems like that. X squared equals nine.
Now, when you had problems like this you
just went and solved it algebraically,
because you knew how to do that. Um, so you
probably took the square root of both
sides and you said that x is going to
equal either plus or minus three. Alright?
Um, the visual of that, if we want to
actually look at the graph, would be
something like this. If we had a
quadratic, Okay? Which means, that little
squared means that it's quadratic.
So that's kind of what we've been studying. Um,
if we take a graph, and this is called
the parabola again.
And you've probably
talked about, you've seen that in
previous videos. Um, this parabola right here
will, will have that shape anytime we
have that squared right there. Okay?
So what we're searching for in this, this
plus or minus three, is we're searching for
these points right here. Where our graph
crosses the x axis.
Um, and in this case it's
you know, the plus or minus three. So we had
our three and our negative three. I know my
graphs pretty, you know, generic there.
But that's what it, you know, essentially
looks like.
Um, so that's what you're doing.
And, and when you have, when you just have
the x squared, solve it algebraically. Okay?
Best way to do it.
But then, um, you probably
saw some, um, um,
equations that might, might have
looked like this. Um, x squared minus 2x, uh, 
minus three. Alright?
And we had to solve these.
And we would say maybe equals zero.
Or equals, um, y. Um,  I put a y there. We'll talk a
little bit about the zero as well.
Um, but when
we have this, you'll notice that we have
the x squared here. But the problem is we
also have an x.
So we have an x squared
and an X. And that makes our lives more
difficult.
It's harder to solve it algebraically.
We can, but we haven't
showed you how to do that yet.
Um< so the best, the way we've showed you how
to do it first is the visual.
The graph. Which is really, really
important. So, this graph real quick, you'd
actually what you would do is you'd create
an xy table. Alright?
And you, you know
plot your points, and eventually, you know
you're searching for, you know, the x
intercepts again.
Um, and your parabola would
look maybe something like this.
It's pretty close but we'd have a root here
in a root here. And again these are
called the roots. Okay?
I don't know if I
just said that. But uh, those are the roots
right there. Okay?
Just like these are the
roots over here. So essentially what
you're searching for is your
x-intercepts, or your roots.
Um, so, that's
what you know how to do. Okay?
And we're
probably pretty good at this. Okay? Not
too bad. We  can graph the points.
And we
can find the roads.
The quadratic formula
will make your lives easier because you
won't have to graph it. Okay? You can
solve, uh, any quadratic equation using the
quadratic formula.
And here is the quadratic formula. Um.
It is negative b plus
or minus the square root of b squared
minus 4ac all over 2a.
And I could write
equals x right here. Alright? Um, so that's
the quadratic formula.
It did derive from something.
And we'll show you how to do
that later. Um, not too concerned about
showing that, that to you yet. But this
quadratic formula, what it will do, is it
will solve any quadratic, um, equation for you.
And some of the, um, next videos I'm
going to, I'm going to play for you.
I'm uh, um, I'm going to show you how to solve some of
these.
Um, and how it works. But just know that
this is it. Okay?
I actually have a student from, um, previ- a 
previous, uh, year create a little video on
it and you can obviously listen to that. I
think you listened to it already. Uh,
But, uh, there's a lot of songs out there if you actually Google quadratic formula songs.
You can hear a lot of people have made
songs up about the quadratic formula.
Uh, just to help them remember, uh, what it is.
So maybe go check out some songs and, um,
definitely memorize this. You should
memorize this formula. um, so again this is um,
this will help us solve any quadratic.
And again, I say it equals the x here, um,
because again, the x's or the x
intercepts we're searching for the roots.
And that's what it will tell us So,
thanks for watching you'll see some, some
of it in later videos, how to use it.
