Negative b
Plus or Minus
The Square Root of b squared
Minus 4 a c
And ALL of this divided by...
2 a
2 a
Negativo b
Más o menos
La raíz cuadrada de b cuadrado
Menos 4 a c
Y todo esto dividido por ...
2 a
2 a
Alright, here we go
we are talking about using the quadratic formula
to solve quadratic equations... alright, so,
First, you will be given a quadratic equation
in STANDARD FORM
and so, that means you're going to have an
x squared term
followed by an x term, followed by a constant
equals ZERO,
preferably,
and in most cases it's going to have to be
equal to zero,
it may say "y ="
but either way you're going to have
the highest degree is going to be x squared
you're going to have an x squared term, a
regular x term
and then a constant term
the coefficients of those terms will be our
"a, b, & c"
So, the first step, will be to identify "a,b & c"
...first thing
So, let's look at the coefficient of the x^2 term
We just have a minus sign there
So, therefore we know
that when we don't have a number...
and we just have a negative sign...
When we don't have a number at all, it's just ONE
But when you have a negative sign
and there's no number, that means it's negative ONE.
So, in our case a is -1
And then, the coefficient to the x term is
positive 3, as you can see
And then the constant that we have is positive 4.
Alright, so we've identified "a, b & c"
The second step is to simply plug "a, b & c"
into the appropriate places in the formula
So, we're starting off with negative "b"...
alright... and so negative "b" will be replaced with 3.
So  it will be negative 3.
We have a positive 3,
but it's going to change to the opposite of a positive 3,
it's going to be a negative 3
Next we have "plus or minus"
That's part of the formula
So, we're going to leave that there
The square root is a par t of the formula
So, we have to keep that..
The next thing we're going to replace is the "b" in b^2
So, we're going to replace that "b" with 3
And so, it's going to be 3^2
Moving right along, ...we've got minus 4
And then we're going to have a and c
And so, "a" is obviously -1
"c" is positive 4
So, we end up with minus "4" times "-1", times "4"
All of this divided by 2a
So, 2a... the "a" is will be replaced by "-1"
And, hey, we've plugged it in to the formula
And now, all we have to do next 
...is SIMPLIFY, this big hairy looking thing
Alright, and so in order to start us off,
we're just going to move from left to right
We're going to start with the -3
Can we simplify that?
No.
So, we're just going to bring it down
It's going to be -3 right there
We're going to keep the plus and minus
the square root of 3^2
So 3^2 is going to be the next thing
We're going to simplify everything underneath the
radical now...
...as a group...we're going to do this together
one at a time...so just moving left to right
3^2... is simply 9
we know that... 3 times 3 is 9
then we have -4 times -1
...that equals POSITIVE 4
POSITIVE 4 times POSITIVE 4 is POSITIVE 16
So we have the square root of 9 + 16 on top so far
..and divided by 2 times -1
...is simply -2
And now we're going to keep simplifying
That's one simplification
We're going to simply it even further
We keep the -3
Plus or minus stays the same
We can go ahead and add 9 + 16 and we get 25
The square root of 25 happens to be a perfect square
We know what that's going to be...
and it's all divided by -2
Moving right along
We have -3 plus or minus
The square root of 5 turned into,..
I'm sorry the square root of 25 turned into 5
divided by -2
Now, it's time to do something with this "plus or minus" 
The "plus or minus" means we're going to have two
different options here
We're going to have -3 + 5 divided by -2
and -3 - 5 divided by -2
So we've got -3 PLUS 5 divided by -2
And we've got -3 MINUS divided by -2
So, simplifying the top there
The top is going to turn out to be
Positive 2, because we had -3 + 5
That's positive 2 on top
and we still have the -2 on the bottom
The other one ends up being -8 on top
because we had -3 minus 5 that time
So that's -8 divided by -2
And we all know that 2 / -2 simply
simplifies to -1
and we have -8 / -2 which is a positive 4
And so our x-intercepts, zeros, roots or solutions
either name will do
is x=-1 and x=4
Negative b
Plus or Minus
The Square Root of b^2
Minus 4 a c
And ALL of this
Divided by
2a
2a
Negativo b
Mas o Menos
la raiz cuadrada de b cuadrado
menos cuatro a c
y todo esto
dividido por
dos a
 dos a
