How many solutions does this quadratic have,
and what are they?
One of math’s strengths is that there is
rarely only one right way to do something.
The Quadratic Formula is just a useful, if
complicated, tool to have in your math arsenal.
We saw this in the Factoring Polynomials video,
but we really didn’t discuss what it is.
This is the Standard Form of a Quadratic Equation.
In many cases, you’ll be able to find its
solutions through factoring, but some quadratic
equations are just too stubborn.
For those, we apply the Quadratic Formula.
The Quadratic Formula is a great tool for
finding solutions when the factors aren’t
likely to be integers or simple fractions,
or for just checking your factors when you
aren’t sure.
It’s one of the most recognizable formulas
in algebra, second only to the Pythagorean
Theorem and the Slope-Intercept Form.
I wish I could tell you there was some easy
way to memorize it, but short of trying to
set it to “Pop Goes the Weasel” you really
just have to struggle through.
Using the formula is marginally easier than
memorizing it.
The variables in the formula correspond to
the coefficients of the Standard Form.
Plug in the numbers, and solve.
You will have to solve it twice, once for
the plus sign and again for the minus sign.
Not all quadratic equations have two solutions.
Before you start pulling out your hair trying
to find solutions, use the discriminant to
figure out how many real solutions you should
be finding.
The discriminant is the expression under the
radical, or b2 minus 4ac.
If the discriminant is positive, there are
two real routes.
If it is zero, there is one real root.
If it is negative, there are no real routes,
which makes sense since we can’t take the
square root of a negative number and get a
real answer.
Now, let’s look at our quadratic equation.
We’ll start by just plugging in our coefficients
and solving for our solutions.
Then, we’ll make sure we have the right
number of solutions by checking the discriminant.
There are two solutions, and they are approximately
1.62 and -0.62.
To 
use the Quadratic Formula to find solutions,
plug in the coefficients from the Standard
Form and solve for both the addition and the
subtraction signs.
