Name__

For use after Chapter 4

For the functiony = -x2 - 6x - 7, find thev6rtex and axis of symmetry.

@ vertex (3, -2); axis of symmetryx = 3

(~ vertex (-3, 2); axis ofsymmetryx = 4

(~ vertex (- 3, 2); axis of symmetry x = - 3

(~) vertex (3, -2); axis of symmetryx =-4

If the graph ely = ax2 + bx + c opensdown, which of the following must be true?

’@ a~0 ® a>0(g) c<O c>O

Which function does not have a maximumvalue?

@ y = -x~ - 5x - 6

(~)y = -xz-2- 6

@’y=3x2- 15x+2

(~)y = 49-x2

4° What is the vertex ofy = -3(x - 2)2 - 4?

@ (-2,-4) (~ (-2,4)

(~ (2,-4) (~ (2, 4)

What are the x-intercepts ofy = -2(x - 7)(x + 2)?

@ -7 and 2 (~) 7 and -2

(~) 14 and -4 (~) 14 and -2

Factor the expression m2 -- 4m - 21.

@(m-7)(m-3) (~ (m-7)(m-3)

(~(m+7)(m-3) (~ (m+7)(m~-3)

Which value ofe makes the expressionX2 -- 5X + ¢ a perfect square trinomial?

5 ¸5

Date _

8. What are the roots of the equationz2 + 11z- 42 = O?

@ -3, 2-14 (~) 3,-14

@ -3, 14 (~ 3, 14

9. Factor the expr~ession gx2 + 28x + 12.

(~ 2(x + 2)(4x + 3)

(~ 2(x + 3)(2x + 1)

@ 4(x + 1)(2x + 3)

(~ 4(x + 3)(2x + 1)

Simplify the expression 22 + x/3"

5

What are the solutions of the equationw2 =

-9. 3 (~ O, -9

(~0,9 (~ 1.9

What are the solutions of23 - 2(x - 3)2 + 7?

(g) _+3 ®

What are the solutions of -3 - y2 = 24?

_+393 ® _+3i (~ ±9~/3 (~) ~9i~

74. What is the standard formi

expression ~i~

1@gi+l

o f the

Alge~]ra 2

Name Date

4For use after Chapter 4

15. What is the absolute value of 3 - 4i?

What is the vertex ofy 3x2 -30x +, 77?

@ (-5. -~2) (~ (-5, 2) ¯

@ (5. -2) (~) (5, 2)

What is the value ofc if the discrimant of-2x2 - 3x + cis 41?

Which’inequality represents the graphbelow?

@ 2x2÷X--15>~O

([~) --2x2 -r-x -- 15_>0

(~D (2x + 5)ix + 3) _> 0

(~ 2x2 --X -- 15 ->0

’ realnumberdoes the ~7x2 - 5:~--have? @

26. A bottle rocket travels along a parabolic pathand reaches a maximum height of 2 r feetafter traveling a horizontal distance of 7.feet.

Write a quadratic function of the formy = a(x - h)2 + k that models thebottle rocket’s path, assuming it leavesthe ground at the point (0, 0).Describe how changing the values ofa, h, and k affect the flight path of thebottle rocket.

ctangular garden is 25 feei

the new

h thegarden by

of the mulch. Writearea of

part (a).do you have to reject?

Chapter 4 Assessment Boo <

Date

For use after Chapter 4

What is the effect on the graph of thefunctiony -- 3x2 4- a when it is (hangedtoy = -3x2 ÷ 4?

@ The graph narrows.

(~) The graph widens.

(~ The graph opens up.

(~) The graph opens down.

~ The vertex moves down the y-axis.

2. What is the minimum or maximum value ofthe functiony = 2x2 - 8x + 5?

(g> y = -3 ® x = -2(~y=2 (~) x= 2(~)y = 29

3. What is the vertex of the graph of thefunctiony = 2(x-4)2 + 6?

@ (-6.4) (~ (-4. -6)@ (--4. 6) (~) (4, 6)(g) (6.4)

What is the axis of symxnetry of the graph ofthe functiony = 7(x + 1)(x - 3]?

What are the roots of the equationy = x2 - 5x - 24?

-3, 8 (~) 3, -8 @ -5, -245,24 @ -6,4

What is the completely simplified expressionfor l~i~?

@ 2~ (~) 4~f8 @ 8~/~

@ liar2 (~) 12~/~

7. Which factorization of4x2 - 19x - 5 iscorrect?

@ 4ix - ll(x -- 5)

~ ~x - ~}(4x + 5)

(~) ~x + 1)(4x - 5]

(1~)(4x- ~)(x + 5~

(~) (4x + [l(x- 5~

What are the solutions of12~(x-3)2+1 = 117

3 3._

3(~)-~-~/~ (~) 3_~2~/5

What is the standard form of the expression(4 3i~ + (-1 - 6i)?

@ 0 (~) -3 - 3i

(~) 3 - 3i (~) 5+9i

(~ 14 -- 27i

16. What complex number is plotted in thecomplex plane?

(~) -2 - 3i

(~) 2 - 3i

(~) 2 + 3i

(~ 3-2i

What are the solutions of 3x2 - 4 = O?

_+~_

+2V~

A~gebra 2Chapter 4 Assessment Book

Name Date

For use after Chapter 4

What is true about the number and type ofsolutions of the equationx2 + 4x - 2 = 0?

@ There are no solutions.

@ There is one real solution.

@ There are two real solutions.

@ There is one imaginary solution.

(~) There are two imaginary solutions¯

pat system of quadratic inequ~,~ties isr ented in the graph?.

15q~l I/I/’,1 I

~x2 + 3~2x2 + 5x - 1~ y > --x2 + 3

14. What is the solution to the quadraticinequality 2x2 - 6x > 5?

~ -0.68_<x_< 3.68

(~) x _< ~0.68 orx _> 3.68

@ x< -3.68 orx_> 0.68

@ 3~i< x<3+i

(~) 3-i 3+ix<~orx> - 2

The vert~of a parabola is (~¢~) andanother p~n the par,ab~]~ is (- 1, - 1).Which point i~<~o ~ t~i~ parabola?

(g) (-l, @ (1, 0)(~) (1. i)

Algebra 258 Chaeter 4 Assessment Book

What is the real partof th{standard formof the~xpression

V(hat i dueof c that mal~

perfect squantrinomial?

A volleyball/playerspikes the b~ll from aheight of 8 ~eet at72 feet per,~econd. Tohe neares htmdredthof a seco~ how longdoes the o~’ther teamhave to prevent the ballfrom h~Rmg the ground.

(23

Date

For use after Chapter 5

2. What is (3.2 × 1.4-X i0-2) written in

4.48 x 107

.8 X 107

3o Which equation is the graph of thepolynomial function shown?

@ f(x) = -2x3 + x2 - 2

(~)f(x)= 3x4-x2+ 1

(~) f(x) = x~ - x + 7

@ f(x) = -2x4 + x~ - 1

What is the degree of the polynomialh(t) = -St2 + 5 - 3t~?

What is the greatest commort monomiaIfactor of9xay2 + 15x2y - 6xy27

@ 3X2 (~) 3y2

@ 3xy @ 3x~y2

Which

7. What is the complete factorization of3x4 -- 3x2?

@ 3x (x --(~ 3x2(x - i)(x + 1)

(g) 3x(x - ~)(x + ~)

@ 3(X4 -- X2)

& Ifx + 3 ~s a factor ofx3 - x2 - 17x - 15,what is another factor?

@x+5 @x-3

Ifx - 2 is a factor ofa polynomialJ(x),which’ of the following statements doesnot have to be true?

@/(2) = 0

@ 2 is a root off(x).

(~) 2 is a zero off(x).

Algebra 2 ’70 Chapter 5 Assessment Book

Name Date

I 5 ~ ForuseafterChapter5

10. Which is not a possible rational solution off(x) = 3x3 - 1 lx2 + 5x - 6? ~,,

-+2 @ ±6

11 ¯ ,on Descartes’which

®o@

possiblefimction

k+4?

0imaginary

12. What is (are) the local minimum value(s)for v(x) = 2x3 -- x2 q- 1?

1

, !and There are none.

13~ ~Iow many solutions does

~m) = -Tin3 - ¢+ 1 have?

continued

14. A greaterthan 12 inches lessthan

volume of a

e onto anr)han

l. Whatshotfld its~havethe

volmne?

15. The numb�math lab is

fstudents who use a collegetcked for several acadennc

years. The ri ~lts are summarized in thetable belov~:

990 ~,1991 1992 1993

$tude~ts ~ 1287 ~365 1402 1693

Y~a, ] 1994 I ii~5 1199611997

Ntadea~ 1952 18;~4 2021 2111

d2 Let 1990 correspondC}p yearx = 0,1991 to yearx = 1 a~4 so on. Enterthe data into your gra~ingcalculator ~d make a ~ :atter plot.~c~ polynomial ~� ton doesR seem to model? Use momialregression to obtain a m~ el. Rmmdto ~o decimN places. ~ at is theregression equation you c [ained?

b. Graph the model and pred{~t what them~ber of students will be 1~ 2006.

c. Graph y = 500 in the same ?~viewing window¯ Find theintersection po~t(s). Explain ~esigNficance of ~our results.

Algebra 2’Chapter 5 Assessment Book

Date

For use after Chapter 5

5?

x5

What is the value of the fi~tionf(x) = 5x3 + x2 - 6x - 4 when x = 2?

@ -4 (~) 8 (~ 20

What is true about the polynomialfunction whose graph is shown?

(~ f(x) ~ -= asx -~

@ Legding coefficient is negative.

(~) Leading coefficient is positive.

4. What is the result when -3x2 x - 2 issubtracted from 4x3 + 2x2 - 6?

(~) --4X3- 5x2-x+ 8

(~ -4x3+x2.x+4

@ 4x3 --x2 --x -- 4

(~4x3+5xz+x-8

~ 7x3 + 3x2 - 8

What is the result when -4x + 5 is cubed?

@ 16x2-40x+25

(~) -64x3 + 125

(~) -64x3 + 240x2 -- 300x -- 125

(~) --12x3 - 120.~a - 300x - 125

(~) -4x3 - 60x2 - 300x + 125

6. What is the complete factorization ofx3 x2-25x-25?

@ (x -- ll(x - 5)(x

® (x - 5)(x@ (x - 1)(xa - 25)

(~) (x 1)(x2 - 25)

(~ tx D(x 25)

What are the real number solutions of theequation 4x5 - 52x3 - 120x = 12x436x27

~ -5.-3.2.4 (~) -5.0.2

(~ -5,2,4 (~ -3. -2.0, 3.5

(~) -2. 0. +-~/~, 5

What is the quotient when9x4 - 45x3 - 37x2 - x2 is divided by9x~ + 1?

@ 6x-2

(~ x2 _ 5x + a _ 6x-29x2 + l

(~ x-Z-5x+a-6x-29x2 + 1

Which is not a possible rational zero of thefunctionf(x) = x4 + 3x3 - 7x2 + 9x - 30?

® -3 @ 1

72Algebra 2Chaeter 5 Assessment Book

Date

CHAPTER

5

How many zeros does the functionf(x) = 2x3 - 6x + 1 have?

@ 1 @ 2 , (~3

(~) 4 (~) -6

What ar~sibl~, n£gativereal zer 3x3 - 5x + 27

Which point is a local maximum of thefunctionf(x) = x4 + 5x3 + x2 - 2x - 6?

@ (-4.76, 0) (~) (-3.57,-51.18).

(~) (-0.47,-5.31) (~) (0.30,-6.37)

(~) (1.05, O)

a cubic function s gr~pli~passeshe points (-5 ,b)~ (-1, 0), (0, 5),

and

g(x) = --X3 -- 2X2 + + 20

What must a group ot

f(x) ,n + c?

(~ Const:~t third-orde

numbers

form

differences

continued

is the value ofthe ~

One zero otf(x) =is xa rational zero

"~ 7. You are ~aking thebottom ~" a gift boxfrom ~!]~iece ofcardbO/ard that is8 in~es by 12 inches.To~e nearest tenthof.~ cubic inch, whatis e maximumv;o~e ~e of the box9

10

Algel~ra 2Chapter 5 Assessment Book 73

Name

For use after Chapter 6

The graph ofy = ~xx is shifted 2 units upand 3 units to the left. Which is the equationof the translated function?

(~)y= x~x+2-3

What are the domain and range of thefunctiony = 5~x - 2?

@ Domain: all real numbers;range: all real numbers

(~ Domain: x _> 2; range: all real numbers

@ Domain: all real numbers; range: y >_ 0 ¯

(~) Domain: x _> 2; range: y _> 0

14. What is (are) the solution(s) to

x-2= Z~I?

(~) x = 1 and 5 (~) No solution

Grinded A~swe~,

15. What is the solution of-2=2?

(D

Whalbe if104

17. Theit cost~

Date

greater

garden

producin~

fuelpricing

t determines thatwidget plus

c~i~t of $2250.

cost function C(x) for

the sharp increase ine led the company’s

to believe thate overall by 10%.

, which

total costC(f(x)) or

y tobefore and

Algel]ra 2 !Chapter 6 Assessrneat Beok " [¯

Name Date

SAT/ACT Chapter" TestFor use after Chapter 6

Which expression has the least v~lue?

@ 812/3 (~) (~)7

What is the value ofx in the equation(x + 3)s = 243?

(~)x = 0orx = 6

(~) x= _+3

(~) x=6

What is the simplest form of the expression(2343)-I/97

@ -2 (~ 8 1/3

1

512

What is the simplest form of the expression+ 10~?

’+ 20~

(~ -64

expression

What isf0~) - g(x) iff(x) =d/2 and

g(x) = (4x~27

Which exp~ionNis ~qual to g(f(x)) iff(x) = x;/1 andg(;~= 6x-27

6

A store that sent you a coupon for 10% off,any i~em has a sale for $5 off all jeans.The pair you want is $39.50. What do youpay if the 10% offmust be applied after the,$5 is taken off?

$3.45 (~ $19.75

(~) $30.55 (~ $30.72

(~) $31.05

What i~ the inverse ofy = Ox -2?

@ Y = 1

(~ y = lO(x

= lO(x + 2)

What is the e of the graph shown?

(~) y = "{ (x-2)

@y (x+2)

1 3

Algebra 2Chapter B Assessment Book 87

Name Date

For use after Chapter 6Chapter Test continued

11. What is the domain and range, respectively,

of the function gtx) = -5

@x>0,y>_0 (~x>-O,y<<.O

@x_<0,y-<0 @x-<0,y->0

@y_>0. x-<0

The graph of which function is shown?

14, 5)

12.

@y=4~x-3

(~y=4~x +3

@y=~-xx-3

The g~aph ofy = 2~xx is shifted down5 units. What is the equation of thetranslated graph?

@y=2~-xx-S

What is the solution of~2xx + 4 = x - 2?

~ 0 (~) -6

@ -~ (i# 2

1~o What is (are) the solutionls) of

x+3 =V~x+41?

(g) -~ ® -s,4@0.4 (~)4

@ No solution

What is the value of8 ~ - ~/~?

the

inverse ofy ~ 1-9

18. What is the extraneoussolution to the equationx-4~xx?

Algebra 288 Chapter6 Assessment Book

Name Date

For use after Chapter8

Which equation represents inverse variation?

(g) yx

y @y=Sx

2. Ifx varies directly withy andy = - 12 whenx = 4, what is the value oily whenx = -3?

~ -16 (~) -9

@9 (~) 16

Let r vary directly with s and inverselywith t. Which equation represents thisrelationship?

Which function represents the graph shown?

X2 -- 9(~)y__~’~ Y = x2 - 9. 7x3

x2 - 9~ Y = x2 - 97x

What is (are) the vertical asymptote(s) of thefunction in Exercise 4?

@x=-3@ x = _+ 3 (~ There are none.

Algebra 2Cha#ter 8 Assessment 8ook

Which function has the domain of alI realnumbers except -2?

@y=X-2 xx+2

= x~ x+2@Y x-2

What are the asymptotes of the fimction4x2 + 3x + _1 ?

Y xz - 1

@x=0, y=0

(~ x = 0, X= 1,y=4

(~x=-l,x=l,y=4

8: What is the simplifi~d form of x 9x+lO?x2+xT6

2x - 5 2x 5

(~) 2x + 5x-3 (~ 2x+5x+3

24a2b13abc

of

The least corrtmon multiple of which pair ofexpressions is 3x(x + 2)(x + 1)?

@ x2 +3x + 2;x q- 2

(~) x2 + 3x + 2; 3x + 6

(~) X2 +3x + 2; 3x2+ 6x

@ x2 +3X + 2; 3x3 + 6x2

Name Date

i) E 8 j For use after Chapter 8

The legs of a right triangle ~e lengthsx~3. What is ~he s~li, fied ratio of

of the triangle t~the hypotenuse?

x

12. Which expression represents the simplified3x - 2

form of 1 5"x - 2 x

G~dded Answer "

What is the solutionof 2 ~_1_9

x-1 x-4’

continued

You~r month

the tot~:~mount y you have,.s for your membership

you

less than 5

A packaging engineer for t~ BubbleBeverage Company is give, the task ofdeserting a new c~. The ~mpany wouldlike ~ minimize the surface area of the canin ord~ to m~imize ov~ll packaging cost.a. Wh~is the surfac~area of a can wi~

radiu~ and heig)~ h? What is thevolum~ an~w~th radius r and ~height #~

f7~. Ifthe ca~ ~ hold 355 mL,determine formNa for the surfacearea of th~~ a in te~s of radius r.(Hint." u~e ~sfact that the volume is355 mL~n, ~ye for h in terms oft.)

~. For wfiat value O~:r is the s~face areaa min~um? Rou~ to one decimal

1d. If~luminum costs th’~company $.001

pd} square cenfimeter;~(~w much willi~ ~ost the company to ~pply thealuminum for the can? ’~

Algel]ra 2Chapter 8 Assessment Book

Name Date

For use after Chapter 8 "

The variable y varies inversely with the cubeofx. Which equation relates x and y?

a

The variable w varies jointly with m an4 nand inversely with t. Which equatiqn relatesw, m, n, and t ?

1~ w = amnt ~ w =

3, What are the asymptotes of the graph of4

y=~+5?

@x= -2,y = 5

(~x=2,y=5

(~x=5,y=2

(~ x=2,y=-5

(~ x=4,y=5

The graph of what function ~s shown?

@y= 1.5x-4 3x-4x-3 (!~ Y=fx+6

@ Y -3x - 4 6x - 42x+6 (~) Y= 2x+3

What is (are) the asymptote(s) of thefunction y - ~5

-- x2 + 3?

(g~x= 0 ®y-0

(~) y = O,x = ~/~

The graph of which function is shown?

-3x2 = 1 --

--3x2

--3x2

@~=x-2

(~Y= x2_4

x~ - 4(~ Y = --3X2 -- 4

What is a simplified form of

16xSy4 o xy2 92y 2x3y7"

¯ @ 4x~y (N5 4x3 @ 4x3

(~) 8x7y8 (~ 8x5y3 + 12x~y~

What is a simplified form ofx+l o (x~ + 2x + 4)?x3 - 8

@x+lx--2

x+l

(~ - ~)(~ + Z, + 4)2

x3 - 8

~ ~2 + 3~_+ ~x3 + x2 + 2x -- 4

Algebra 2Chapter 8 Assessment Book

Date

For use after Chapter

Which expression is equivalent to¯ 4x ox2+39x+3 x2-9’

(~) -x+ 1

4x(x~ + 3)® (x - 3)(x + 3)~

( x+ 1)(x-3)(~) (-x - 3)(x -,4~

(~) 3(x2-4x-1)

(x - 3)(x + 3)!

What expression is equivalent to2

x+ 11 5"

x+l x

2x+ 1~

2x 2x® 2 + 5(x+l) ® 6x+5

2(6x+5)® 2(x+ 1)2

What is the Solution of

4 32x+l x-3’

What is (are) the solution(s) of-(x + 4) -4 9

x x-2’

@ --2 ® --2, 4 ® 4

®2 ®2,-4

13. The variablex variesjointly withy and z,and x = 8 wheny = -6 andz = -3.What is the constantof variation?

What is the simplestform of

X2 + 8X 2X2 + 15X -- 8?4X 2X -- 1

What is the extraneoussolution of3 9 = _7?x 4 x

@

(!)

A~gehra 2Chapter 8 Assessment Book 121