Name
LESSON
5-4
Date
Class
Practice B
Completing the Square
Solve each equation.
1. 2x 2  6  42
2. x 2  14x  49  18
Complete the square for each expression. Write the resulting
expression as a binomial squared.
3. x 2  4x 
4. x 2  12x 
Solve each equation by completing the square.
5. 2d 2  8  10d
6. x 2  2x  3
7. 3x 2  18x  30
8. 4x 2  12x  4
Write each function in vertex form, and identify its vertex.
9. f  x   x 2  6x  2
10. f  x   x 2  4x  1
11. h  x   3x 2  6x  15
12. f  x   2x 2  16x  4
Solve.
13. Nathan made a triangular pennant for the band booster club. The area of the
pennant is 80 square feet. The base of the pennant is 12 feet shorter than the
height.
a. What are the lengths of the base and height of the pennant?
b. What are the dimensions of the pennant if the base is only 6 feet shorter than the height?
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c05-4_pr.indd 28
28
Holt Algebra 2
12/7/05 10:30:29 AM
,%33/.
x‡{
*À>V̈ViÊ
#OMPLETINGTHE3QUARE
x‡{
3OLVEEACHEQUATIONUSINGSQUAREROOTS
3OLVEEACHEQUATION
SXD SXD X r X r ^
*À>V̈ViÊ
#OMPLETINGTHE3QUARE
--"
SXD ^
X
XOR
X
XOR
S D
X
XOR
S D
S D
??
E T???
E T???
S D
X X B 3IMPLIFY
X X
C &ACTORTHESQUARE
SX
D 4AKESQUAREROOTOFBOTHSIDES
X
DSX D Êr £ÎÊ
XÊÊÚÚ
ÊÎÊÊÊÊÚÚÚÚ
Ê ÊÊ
ÊÊ
Ó
Ó
FSXDX X
FTXEÊÊÊÊTXÎÊEÊÓÊ££ÆÊÊÊTÎ]Ê££ÊEÊ
X
^
^
XÊÊÎÊÊÊr£™ÊÊ
HSXDXX
X X
^
X X
X X
XÊÊÎ]Ê£
X X
FSXDX X
^
X r E 3OLVEFORX
DÊÊÊÚÚ
ÊxÊ ÊÊÊ Ê Ê
ÊÊ
Ó
Ó
7RITEEACHFUNCTIONINVERTEXFORMANDIDENTIFYITSVERTEX
p^^^
X X
^
Êr {£ÊÊ
ÚÚÚÚ
X X
B TOEACHSIDEOFTHEEQUATION
A !DD ??
D D
ÊÊÊTXÊÊÈÊEÊÓÊ
3OLVEEACHEQUATIONBYCOMPLETINGTHESQUARE
???
3OLVEEACHEQUATIONBYCOMPLETINGTHESQUARE
Xr
ÊÊTXÓÊ Ê Ê
X X
S D
EÓ
ÎÈ
XX
X X
??
{
X X
X X
XÊÊÇÊÊÎÊrÓÊÊ
#OMPLETETHESQUAREFOREACHEXPRESSION7RITETHERESULTING
EXPRESSIONASABINOMIALSQUARED
4OCOMPLETETHESQUAREOFX BXADD ??
B TOTHEEXPRESSION7RITE
THETERMNEEDEDTOCOMPLETETHESQUAREFOREACHEXPRESSION
^
^
XÊÊÓÊrÈÊÊ
XX
X ^
X r GTXEÊÊÊÊTXÓÊEÊÓÊÎÆÊÊÊTÓ]ÊÎÊEÊ
FSXDXX
HTXEÊÊÎÊÊTX£ÊEÊÓÊ£nÆÊÊÊT£]Ê£nÊEÊ
FTXEÊÊÓÊÊTXÊÊ{ÊEÊÓÊÊÎÈÆÊÊÊT{]ÊÎÈÊEÊ
3OLVE
3OLVE
.ATHANMADEATRIANGULARPENNANTFORTHEBANDBOOSTERCLUB4HEAREAOFTHE
PENNANTISSQUAREFEET4HEBASEOFTHEPENNANTISFEETSHORTERTHANTHE
HEIGHT
2ALPHAND%DIEEACHSOLVEDTHEEQUATIONSXD 2ALPHSAYSTHECORRECTANSWERISX%DIESAYSTHECORRECTANSWER
ISX7HOISCORRECT(OWDOYOUKNOW
A 7HATARETHELENGTHSOFTHEBASEANDHEIGHTOFTHEPENNANT
4HEYAREBOTHCORRECT0OSSIBLEANSWER!QUADRATICCANHAVETWOPOSSIBLE
SOLUTIONSXSOX
>ÃiÊÊnÊvÌ]ʅiˆ}…ÌÊÊÓäÊvÌ
B 7HATARETHEDIMENSIONSOFTHEPENNANTIFTHEBASEISONLYFEETSHORTERTHANTHEHEIGHT
>ÃiÊÊ£äÊvÌ]ʅiˆ}…ÌÊÊ£ÈÊvÌ
#OPYRIGHT©BY(OLT2INEHARTAND7INSTON
!LLRIGHTSRESERVED
--"
x‡{
(OLT!LGEBRA
*À>V̈ViÊ
#OMPLETINGTHE3QUARE
x‡{
#OMPLETETHESQUAREFOREACHEXPRESSION7RITETHERESULTING
EXPRESSIONASABINOMIALSQUARED
n£
XX
TX££ÊEÊÓÊ
9OUCANUSETHESQUAREROOTPROPERTYTOSOLVESOMEQUADRATICEQUATIONS
ÚÚÚ
Ê ÊÊÊ
3QUARE2OOT0ROPERTY
{
T
4OSOLVEXA
X A
TAKETHESQUAREROOT q^
X q^
A
OFBOTHSIDESOFTHE
X
q^
A
EQUATION
™Ê ÊÓÊ
ÊÊÊ XÊÊÊÊÚÚ
Ó
E
3OLVEEACHEQUATIONBYCOMPLETINGTHESQUARE
^
^
XÊÊÓÊÊÊrÎÊÊ
X X
Xq q
T
E
^
SXD q 4AKETHESQUAREROOTOFBOTHSIDES
q
^
T
3IMPLIFY
^
T
E
E
^
^
^
3OLVEEACHEQUATION
X
X XX
SX
FTXEÊÊÊXÊÓÊÈXÊÊ£ä
Xr
^
Xr
Y‡ˆ˜ÌiÀVi«ÌÊÊ£Ç
^
Xr
X X X
X TXE
X
Xr
^
^
^
£ÎÆÊTÊÈ
D ^
X 3TTEÊÊÊÊTTÎÊEÊÓÊÊ{
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
^
4HINKq q q q
q ^
^
3UBTRACTFROMBOTHSIDES
^
Xq
4HEVALUEOFASTOCKISGIVENBY3STDTTWHERETISTHENUMBER
OFDAYSAFTERTHEPURCHASE
C 7HATISTHEVERTEX7HATDOESTHEVERTEX
REPRESENTINTERMSOFTHESTOCKPRICE
^
&ACTORTHEPERFECTSQUARETRINOMIAL
Xq
B 7HATISTHEVALUEOFTHESTOCKATT!TWHAT
OTHERTIMEWILLTHESTOCKHAVETHISSAMEVALUE
^
^
Xq
3OLVE
#OPYRIGHT©BY(OLT2INEHARTAND7INSTON
!LLRIGHTSRESERVED
E
ÎÊ ÊÓÊÊÊÊÚÚÚ
xÇÊÊÊÆÊÊÊ ÊÚÚ
ÎÊ]ÊÊÊÚÚÚ
xÇÊÊÊ Ê
FTXEÊÊ XÊÊÊÊÚÚ
{
Ó
Ó {
A #OMPLETETHESQUAREANDWRITETHE
FUNCTIONINVERTEXFORM
^
SXD FSXDX X
7HATISTHEYINTERCEPTFORTHEGRAPHOFTHE
FUNCTIONFSXDSXD ^
4HINKqq
q q
q T
7RITEAQUADRATICEQUATIONWITHTHEVERTEXSD
ANDAINSTANDARDFORM
3IMPLIFY
3OLVE X X
£xÊÆÊÊÊ ÚÚ
£xÊ Ê
£Ê ÊÓÊÊÊÊÚÚÚ
GTXEÊÊÊÊ XÊÊÊÚÚ
Ê£Ê]ÊÊÊÊÚÚÚ
{
£È { £È
HTXEÊÊÎÊÊTX{ÊEÊÓÊÎÎÆÊÊÊT{]ÊÎÎÊEÊ
4AKETHESQUAREROOTOFBOTHSIDES
HSXDX X
^
Xq
FTXEÊÊÊÊTXÓÊEÊÓÊÓ£]ÊÊÊTÓ]ÊÓ£ÊEÊ
$IVIDEBOTHSIDESBY
^
^
FSXDX X
AK4up.indd 81
X ^
GSXDX ??
X
4HECOEFFICIENTOFX SHOULD
BETOUSETHESQUAREROOT
PROPERTY
!DDTOBOTHSIDES
Xq
7RITEEACHFUNCTIONINVERTEXFORMANDIDENTIFYITSVERTEX
X
^
XÊÊ{ÊÊÓÊrÎÊÊ
X X
XÊÊ£]Ê{
ANDSD
X X
XÊÊÇÊÊÊrÇÎÊÊ
2EMEMBER
3OLVE X XX œÌʏ}iLÀ>ÊÓ
,iÌi>V
#OMPLETINGTHE3QUARE
,%33/.
X X £Ó£ #OPYRIGHT©BY(OLT2INEHARTAND7INSTON
!LLRIGHTSRESERVED
Xr
Xr
ÊTÎ]Ê{ÊEÊÆÊ̅iʓˆ˜ˆ“Õ“Ê«ÀˆVi
œÌʏ}iLÀ>ÊÓ
#OPYRIGHT©BY(OLT2INEHARTAND7INSTON
!LLRIGHTSRESERVED
81
(OLT!LGEBRA
Holt Algebra 2
5/20/06 2:38:46 PM