Let's do a quick review
of the quadratic formula,
as you might see it
used in physics courses.
Now in your math
classes, you commonly
see the quadratic formula in
this sort of a situation, where
you've got numbers for a, b,
and c, some sort of variable,
often x, listed as x squared,
x, and then no variable there.
In physics, you might see
something that looks like this.
It may not look like
it's exactly the same,
but if you do some basic algebra
on it, rearrange the terms,
you end up with an
equation of this form.
So this may be a situation
where, again, I've got numbers
for a, b, and c, I've
got a variable squared
to the first power, this
is a quadratic equation.
Quadratic formula says if I
have an equation of that form,
then I can find the solution,
the value for x, using this.
And in general,
there's two solutions
for every quadratic
equation, and one of them
is found when you've got the
plus sign, and one of them
is found when you're
using the negative sign,
so you actually solve
this equation twice.
Let's take an example of that
with our physics equation
that we just had a moment ago.
First thing you realize is that
we're solving for t, not for x.
But if I look at
our basic equation,
I can pull my numbers out, and
I find my a, my b, and my c
by looking at the
appropriate terms.
If I take that, realizing that
I've got my values that I'm
solving for, my variable my
a, my b, and my c numbers,
I can then plug them in
to my quadratic solution.
And for this one, I end up
with this sort of a format.
And again, you can pause
the video at this point
and actually plug stuff in
and look at it for yourself,
but instead of x, I've got t.
I'm plugging in for my b, my
b squared, my a, my c, my a,
plugging in all of those values.
Once you've got all those
things plugged in, then
you want to start simplifying.
Taking that same equation
up here at the top,
we can see that we
can start simplifying.
If you've got minus
signs out here,
two minus signs make a positive.
My number that I've got
squared, and my other numbers, I
can multiply those out.
Do be careful on
this squared here
because if your b
is negative, it's
the negative number
that's squared,
so it's negative 2.3
times negative 2.3.
And so that should always
give you a positive number.
Taking it just a little bit
further in my simplification,
I can add up those two
numbers, take the square root,
and that's going
to give me a value.
Again, as a caution, what you've
got underneath the square root
must be a positive number.
If it's not a positive
number, you've
either made a mistake
in your algebra,
or you've got bad numbers.
Once we've got it
down to this form,
we can solve it first with a
plus and then with the minus.
So for these
particular numbers, you
should get these two solutions.
And I encourage you
to pause the video,
plug it into your
own calculator,
and find your answers.
There's something that goes a
little bit beyond math here.
In math these are just the
two possible solutions.
In physics, these two
solutions have meaning.
So in this case,
if this is time,
the fact that I've got one
answer positive and one
answer negative means
this is the answer which
happened after the
start of the event,
and this is a time
where I'd have
the same physical
conditions, but it actually
is before the
start of the event.
So sometimes using a
little bit of common sense,
you can figure out which of
the two solutions is correct,
but there's always going
to be two solutions.
We're going to use the
quadratic formula as we're
solving physics problems
throughout the semester,
so if you're not really
familiar with it,
you might want to practice up.
Again, go back
through the video,
pause it where you need to,
plug-in some different numbers,
calculate it out,
and make sure you're
getting the same answers.
