Solving Quadratic Equations
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1Thetli
You
found the
greatest
common
factors
of
sets
of
numbers.
Nbur
.
Write quadratic
equations
in
intercePt
form.
.
Solve
quadratic
equations by factoring.
Standards
A2.l.s
Solve
problems
that
can be
modeled
using
quadratic equations
and
functions, interpret the
solutions, and determine
whether the solutions
are
reasonable.
A2.4.7
Find a
polynomial
{unction of lowest
degree
with
real coefficients given its roots
and
use
the relationship
between solutions of
an
equation, zeros of
a
function,
x-intercepts of
a
graph
and
factors of
a
polynomial
expression
to
solve
problems.
DlSw
v**elislbs!tr
factored form
FOIL
method
Related Graph
2
and
6
are
r-intercepts.
-5
as
its roots.
)
eersonal
Tutor
i--1-
e-*--"**--------'
'
glencoe,com
fl-.cria"a
Practice
t.
W.it"
a
quadratic equation
in standard form with
f
a"d
26A
Chapter
5
Quadratic
Functions
and
Relations
Solving Quadratic Equations
by Factoring
The
factored
form of
a
quadratic equation is
0
:
a(x
-
p)(x
-
4).
In
the equation,
p
and
4
represent
the
x-intercepts of the graph of the equation.
The
r-intercepts of the graph at the
right
ate
2
and
6.
In this
lesson,
you
will
learn
how to
change
a
quadratic equation
in
factored
form into
standard
form
and vice
versa.
Standard Form
0=x2-8x*12
FaCtOfed
FOfm You
can use
the FOIL
method to
write
a
quadratic equation that is
in
factored
form in standard form.
The
FOIL method
uses
the
Distributive Property to
multiply
binomials.
W'write
an Equation Given
Roots
"
w.it"
a
quadratic equation
in
standard
form with
-]
and
6 as
its roots.
(x
-
p)(x
- il
=
0
WritethePattern'
[,
-
(-*)]O
-
6)
=
0
Reprace
r
with
-]
and
s
with
5.
(,*1)O
-6):o
simprirv.
,2-17r-)=O
Multiply.
^:
3x2
-17x
- 6:0
Multiplyeachsidebylsothat
bandc
areintegers'
E
yl
t'
"i
,,
I
+',
rO
i:
l
.
Factored Form
0:
(x
-
6l(,x
-2\
FOII Method
for Multiplying
Binomials
Words
To multiply
two
binomials,
find the sum of the products of
F
the Firsf
terms, O the Outer terms,
t
the
tnner terms, and L the
losf
terms'
Examples
Product
of
First
Terms
J
)
:
(x)E)
Outer
Terms
lnner
Terms
Last
Terms
=
x2
-
2x
-
6x
*
12 or x2
-
8x
+
12
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