This video is going to be about finding a quadratic equation when you're
given the roots, or the solution, of that
equation.
So here's what it's about.
Let's say you're told that there's a quadratic equation
and the roots, or the solution,
is going to be x equals
negative 2
and 4.
Well, I could rewrite this as
two equations.
x = -2 and x = 4.
And then if I wanted to, I could take the
equation on the left, x = -2,
I could add 2 to both sides
and I would end up with
x + 2
equals zero.
And on the right side, where I have x = 4, 
I could subtract 4
and I would have x - 4
equals zero.
So now, if x + 2 equals zero and
x - 4 equals zero, then when I multiply
the two of them together, they would also
have to equal zero.
So I'm just going to say
x + 2
times
x - 4
equals zero.
and instead of leaving that in factored form,
I'm going to multiply it out to simplify
it.
So I'll have x times x is x-squared,
x times negative 4 is negative 4x,
2 times x is 2x,
and
2 times negative 4 is negative 8.
and that whole thing
equals zero.
And now I'll just combine the like terms that I have. So I end up with x-squared,
negative 4x plus 2x is negative 2x,
negative 4x plus 2x is negative 2x,
minus 8
equals zero.
So let's see what I've got here.
I've got a quadratic equation
and the solutions to this equation
are going to be what I started with.
If you think about what I have,
If I look at this whole process
moving upwards,
it's like saying
you're given a quadratic equation,
factory it so you get the solutions.
All I've done,
in a sense,
is "un-factor" it,
so that I would get the equation.
So that's the whole process. 
Let me just review it because it's really
that simple.
If you've given
the solutions, or the roots,
to an equations...
you may be given it in this form, 
x = -2 and positive 4, you may be told
that the graph of the equation goes
through the points...
let's see, I guess that would be, 
if x equals negative 2,
then
on a graph
we would have the equation going through the point (-2, 0)
and also through the point
(4, 0).
In other words, that would be the
horizontal intercepts.
So you might have given it as a horizontal
intercept, or you might just be told these 
are the solutions or real roots, 
or the zeros.
All you do
is you take
those two solutions
you set each one equal to x,
then you
rearrange each equation
so that you have x plus or minus something
equals zero.
then you take those two equations and
multiply them together, since if they
both equal zero, then their product will
equal zero.
And then after you've multiplied it, you just go
through the process of combining like
terms, simplifying it down and so on, 
and you've got an equation
with the solutions that you were given to begin with.
So that's it.
Take care, 
I'll see you next time.
