9-1 Practice A Identifying Quadratic Functions

944 downloads 5405 Views 152KB Size Report
Holt Algebra 1. All rights reserved. Name. Date. Class. LESSON. 9-1. Practice A. Identifying Quadratic Functions. Tell whether each function is quadratic. Explain ...
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

TX YE

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

DOWNWARD A A 



Õ«Ü>À`



UPWARD A A







 '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]ÊAÊ Êä

&OREACHPARABOLA A IDENTIFYTHEVERTEXB GIVETHEMINIMUMOR MAXIMUMVALUEOFTHEFUNCTIONC FINDTHEDOMAINANDRANGE 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 DIFFERENCESINY VALUES )FTHESECONDDIFFERENCESARE CONSTANT THENTHEFUNCTIONIS QUADRATIC

Y     

   

     

 TE TE TE

QUADRATICTHESECONDDIFFERENCEARECONSTANT





X



#OPYRIGHT©BY(OLT 2INEHARTAND7INSTON !LLRIGHTSRESERVED

X     

SD  SD      









3TEP&INDTHEFIRST DIFFERENCESIN Y VALUES)FTHEYARE CONSTANT THEFUNCTION ISLINEAR







  SD









Õ«Ü>À`]ÊAÊÊ{]ÊAÊÊä



SD SD  SD

4HISFUNCTIONISQUADRATICBECAUSETHESECONDDIFFERENCESARECONSTANT

 YXX

 X XY

Y     

4ELLWHETHEREACHFUNCTIONISQUADRATIC%XPLAIN

4ELLWHETHERTHEGRAPHOFEACHQUADRATICFUNCTIONOPENSUPWARDOR DOWNWARD%XPLAIN



3TEP#HECKFORA CONSTANTCHANGEIN X VALUES#ALCULATETHE SECONDVALUEMINUSTHEFIRST

 

(OLT!LGEBRA









X     







MINIMUM

C $ALLREALNUMBERS2Y

,iÌi>V… )DENTIFYING1UADRATIC&UNCTIONS

SD SD SD 

Y   YX ??  





B

4ELLWHETHERTHISFUNCTIONISQUADRATIC%XPLAIN

Þià ˆÌÊV>˜ÊLiÊÜÀˆÌÌi˜Êˆ˜Ê̅iÊvœÀ“Ê YÊÊÊAXÊÓÊÊBXÊÊV°



      

A



4HEREARETHREESTEPSTOIDENTIFYAQUADRATICFUNCTIONFROMATABLEOF ORDEREDPAIRS



'RAPHEACHQUADRATICFUNCTION Y  X   Y??  



T E

#OPYRIGHT©BY(OLT 2INEHARTAND7INSTON !LLRIGHTSRESERVED

™‡£





A

 X Y

̅iÊÃiVœ˜`Ê`ˆvviÀi˜ViÃÊ>ÀiʘœÌÊVœ˜ÃÌ>˜Ì°



X





,%33/.



       





4ELLWHETHEREACHFUNCTIONISQUADRATIC%XPLAIN





T E

*À>V̈ViÊ

)DENTIFYING1UADRATIC&UNCTIONS

 S D S D S D S D





X







#OPYRIGHT©BY(OLT 2INEHARTAND7INSTON !LLRIGHTSRESERVED

      







X



5SETHEGRAPHOFTHEQUADRATICFUNCTIONBELOWFORQUESTIONS















&OREACHPARABOLA A IDENTIFYTHEVERTEXB GIVETHEMINIMUMOR MAXIMUMVALUEOFTHEFUNCTIONC FINDTHEDOMAINANDRANGE







 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

 S D S D S D S D

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(OLT 2INEHARTAND7INSTON !LLRIGHTSRESERVED

75



X

Y

























NOTQUADRATIC





ITISLINEAR



(OLT!LGEBRA

Holt Algebra 1

5/9/06 1:19:48 PM