Name
Date
Class
Practice A
LESSON
9-1
Identifying Quadratic Functions
Tell whether each function is quadratic. Explain.
1.
x
1
2
3
4
5
y
0
3
8
15
24
2. y 5 2x
2
yes
yes
it can be written in the form
y ax 2 bx c.
the second differences are constant.
Y
3. Use the table of values to graph y x 2 4.
yx 4
2
x
2
1
0
1
2
x,
y
y 2 2 4 0 2, 0 y 1 2 4 3 1, 3 y 0 2 4 4 0, 4 1, 3 y 1 2 4 3
2
2, 0 y 2 4 0
X
Tell whether the graph of each quadratic function opens
upward or downward.
4. y 5x 2
5. y 2x 2 7
downward
upward
Use the graph of the quadratic function below for questions 68.
6. Identify the vertex of the parabola.
Y
2, 6 7. Give the minimum or maximum value.
X
minimum: 6
8. Find the domain and range.
D: all real numbers; R: y 6
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a107c09-1_pr.indd 3
3
Holt Algebra 1
12/20/05 5:52:59 PM
Process Black
*À>V̈ViÊ
)DENTIFYING1UADRATIC&UNCTIONS
--"
™‡£
™‡£
4ELLWHETHEREACHFUNCTIONISQUADRATIC%XPLAIN
4ELLWHETHEREACHFUNCTIONISQUADRATIC%XPLAIN
X
Y
ÞiÃ
YX
TXYE
YÊÊÊÊTÓÊEÊÓÊÊ{ÊÊä
YÊÊÊÊT£ÊEÊÓÊÊ{ÊÊÎ
YÊÊÊÊTäÊEÊÓÊÊ{ÊÊ{
YÊÊÊÊT£ÊEÊÓÊÊ{ÊÊÎ
YÊÊÊTÓÊEÊÓÊÊ{ÊÊä
TÓ]ÊäÊEÊ
T£]ÊÎÊEÊ
ÊTä]Ê{ÊEÊ
ÊT£]ÊÎÊEÊ
TÓ]ÊäÊEÊ
X
X
X
Y
Y
4ELLWHETHERTHEGRAPHOFEACHQUADRATICFUNCTIONOPENS
UPWARDORDOWNWARD
`œÜ˜Ü>À`
X Y
DOWNWARDAA
Õ«Ü>À`
UPWARDAA
'IVETHEMINIMUMORMAXIMUMVALUE
TÓ]ÊÈÊEÊ
Y
)DENTIFYTHEVERTEXOFTHEPARABOLA
Y
Y
X
“ˆ˜ˆ“Õ“\ÊÈ
&INDTHEDOMAINANDRANGE
\Ê>ÊÀi>Ê˜Õ“LiÀÃÆÊ,\ÊYÊÊÈ
--"
™‡£
œÌʏ}iLÀ>Ê£
˜œ
B
MAXIMUM
C $ALLREALNUMBERS2 Y X
X
`œÜ˜Ü>À`]ÊAÊÊx]ÊAÊÊä
&OREACHPARABOLAAIDENTIFYTHEVERTEXBGIVETHEMINIMUMOR
MAXIMUMVALUEOFTHEFUNCTIONCFINDTHEDOMAINANDRANGE
Y
Y
X
A
ÊTÎ]ÊxÊEÊ
B
“ˆ˜ˆ“Õ“\Êx
C
\Ê>ÊÀi>Ê˜Õ“LiÀÃÆÊ,\ÊYÊÊx
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
AK4up.indd 75
3TEP&INDTHESECOND
DIFFERENCESINYVALUES
)FTHESECONDDIFFERENCESARE
CONSTANTTHENTHEFUNCTIONIS
QUADRATIC
Y
TE
TE
TE
QUADRATICTHESECONDDIFFERENCEARECONSTANT
X
#OPYRIGHT©BY(OLT2INEHARTAND7INSTON
!LLRIGHTSRESERVED
X
SD SD 3TEP&INDTHEFIRST
DIFFERENCESIN
YVALUES)FTHEYARE
CONSTANTTHEFUNCTION
ISLINEAR
SD
Õ«Ü>À`]ÊAÊÊ{]ÊAÊÊä
SD
SD
SD
4HISFUNCTIONISQUADRATICBECAUSETHESECONDDIFFERENCESARECONSTANT
YXX
X XY
Y
4ELLWHETHEREACHFUNCTIONISQUADRATIC%XPLAIN
4ELLWHETHERTHEGRAPHOFEACHQUADRATICFUNCTIONOPENSUPWARDOR
DOWNWARD%XPLAIN
3TEP#HECKFORA
CONSTANTCHANGEIN
XVALUES#ALCULATETHE
SECONDVALUEMINUSTHEFIRST
(OLT!LGEBRA
X
MINIMUM
C $ALLREALNUMBERS2Y
,iÌi>V…
)DENTIFYING1UADRATIC&UNCTIONS
SD
SD
SD
Y
YX ??
B
4ELLWHETHERTHISFUNCTIONISQUADRATIC%XPLAIN
ÞiÃ
ˆÌÊV>˜ÊLiÊÜÀˆÌÌi˜Êˆ˜Ê̅iÊvœÀ“Ê
YÊÊÊAXÊÓÊÊBXÊÊV°
A
4HEREARETHREESTEPSTOIDENTIFYAQUADRATICFUNCTIONFROMATABLEOF
ORDEREDPAIRS
'RAPHEACHQUADRATICFUNCTION
Y
X Y??
TE
#OPYRIGHT©BY(OLT2INEHARTAND7INSTON
!LLRIGHTSRESERVED
™‡£
A
X Y
̅iÊÃiVœ˜`Ê`ˆvviÀi˜ViÃÊ>ÀiʘœÌÊVœ˜ÃÌ>˜Ì°
X
,%33/.
4ELLWHETHEREACHFUNCTIONISQUADRATIC%XPLAIN
TE
*À>V̈ViÊ
)DENTIFYING1UADRATIC&UNCTIONS
SDSDSDSD
X
#OPYRIGHT©BY(OLT2INEHARTAND7INSTON
!LLRIGHTSRESERVED
X
5SETHEGRAPHOFTHEQUADRATICFUNCTIONBELOWFORQUESTIONS
&OREACHPARABOLAAIDENTIFYTHEVERTEXBGIVETHEMINIMUMOR
MAXIMUMVALUEOFTHEFUNCTIONCFINDTHEDOMAINANDRANGE
YX YX YX 4ELLWHETHERTHEGRAPHOFEACHQUADRATICFUNCTIONOPENSUPWARDOR
DOWNWARD%XPLAIN
X
??
??
Y
ITCANNOTBEWRITTENINTHEFORM
YAXBXC
THESECONDDIFFERENCESARECONSTANT
NO
5SEATABLEOFVALUESTOGRAPHEACHQUADRATICFUNCTION
X YX Y??
Y
Y
5SETHETABLEOFVALUESTOGRAPHYX
X
YES
ˆÌÊV>˜ÊLiÊÜÀˆÌÌi˜Êˆ˜Ê̅iÊvœÀ“Ê
YÊÊÊAXÊÓÊÊBXÊÊC°
̅iÊÃiVœ˜`Ê`ˆvviÀi˜ViÃÊ>ÀiÊVœ˜ÃÌ>˜Ì°
XY
SDSDSDSD
ÞiÃ
YX *À>V̈ViÊ
)DENTIFYING1UADRATIC&UNCTIONS
,%33/.
A
ÊT£]ÊxÊEÊ
B
“>݈“Õ“\Êx
C
\Ê>ÊÀi>Ê˜Õ“LiÀÃÆÊ,\ÊYÊÊx
œÌʏ}iLÀ>Ê£
X
Y
NOTQUADRATIC
THESECONDDIFFERENCESARENOT
CONSTANT
#OPYRIGHT©BY(OLT2INEHARTAND7INSTON
!LLRIGHTSRESERVED
75
X
Y
NOTQUADRATIC
ITISLINEAR
(OLT!LGEBRA
Holt Algebra 1
5/9/06 1:19:48 PM