Hello. I'm Professor Von Schmohawk
and welcome to Why U.
In the previous lecture
we introduced "quadratic functions".
We saw that a "quadratic function of x"
is any function which can be defined by the
expression "a x-squared, plus b x, plus c"
where a, b, and c are constants
which determine the shape and position
of the function's graph.
We also saw that although
the constants b and c can be zero
in order to be a quadratic function,
the constant "a" must not be zero.
A quadratic expression can be created by
multiplying two linear expressions together.
As an example,
let's multiply two linear expressions
"3x + 4"
and "2x + 1".
We can expand the product of the two binomials
using the distributed property.
To do this, we must multiply each term
in the first binomial
times each term in the second binomial
and add the resulting products.
These products can be created in any order
as long as individual products are formed
by multiplying each term in the first binomial
times each term in the second binomial.
The order of multiplication we will choose
is called the "FOIL" method.
FOIL is an acronym which stands for
multiplying the first terms of the two binomials
then the outer terms
then the inner terms
and finally, the last terms.
Once we have produced these four products,
we can combine the two x terms
giving us the quadratic expression
"6 x-squared + 11x + 4".
So using the FOIL method,
this product of binomials was produced
by multiplying the first terms
the outer terms
the inner terms
and the last terms of the two binomials.
Since the quadratic expression
"6 x-squared + 11x + 4"
is the product of the two
linear expressions
"3x + 4"
and "2x + 1"
"3x + 4" and "2x + 1" are factors
of that quadratic expression.
In later lectures, we will learn several methods
of factoring quadratics
including "factoring special products"
"factoring by inspection"
and "factoring by completing the square".
In addition, we will see how
any quadratic function
can be factored into two linear functions
through the use of the quadratic formula.
But before we study methods of factoring
in the next lecture we will examine two
different ways to write quadratic functions
and see how those forms
are related to the function's graph.
