Atgebra
?
Name
SfudY Guide ChaPter 5
Iliimtions: Show all wq$i and r,qeqo4irts to rtceive full credit
Idenfify the quadraticr linear and constant terils. Detemine whether each function is linear or quadratic-
7(x-z)+5(3x)
ff*)= Zx-tl +/Sx
,.,=t@r)-l*
1: ff+ly.3x-t'-*{
/,n rrr 6^.],*n
v;= x-tt
[,,-eo, 6^],**,
1.,(x)=
pa)=eox*tr
I
Vertex:
:
Yertex:
)
{*, *#}
.;
(-{ , r}
:
,
j
;
!
:
Axis of $ymmetry:
Axis of Spnmctry:
;
-3
i:
xxv
r3
;:
;:
-?
:;
'.
;;
,;
:i
:
,.
t,,
,M=#
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...:;." ." ...::."
.:. .... . ... ' ).. -.
1
i
.."
\;
:i
....
f,'or problems 5 and 6:
$
Wrin eachfunction in
vertafonn SfiOlyALL WORX.
its vertex md y - interaqt (whieh will
U\ erupn ,*iyuoaion using
5. v= t' -2x-3
xx-*.
m.&ffi
*'l
*
3 {r}8*s{t}*S =
t**,) 3-q
33
verrex: (ttry Y)
y*inrercepr:
(O1* -$)
he evidentfrom
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......
.-,
..
. ..
.,.
,
..
).. , .......
.,
"
vefiaform).
*b+2
""*;3- *# *)
f=*3; -L 7
*1
6. y= -*
p {'*}}
F;
$
u
* -(n)'+#{r} #P
d
f*{
4
66*J
1
I
I,4;
i
b(H#
J
vertex' ( 1 ) 3)
y*intercept:
(n ? a)
rlu+ *
6
*f
Graph each quadrafic function using the requested informaticn.
7.
y+7=*
8.
r,
1-- Xr_T
Up or down (answer only):
Vertex (work and answer).
Up or down (ansyer onlY): LJ P
JttT'H-f:'-u' {*,*?}
2a
1a
y
-
f,: i,D,=
t\
h'r
e(ti
Y=f +2x+6
P
{o}}-J # *T
r' t
J
*"{n,*
Y
Attendance
196*
{thousands}
4962
5234
1963
l/u? o #
r964
1965
Factor each qundratic #xpressign ccmpletely'.
10.
Year
L96L
1962
What does your equation predict the attendance will be in yfrar L*?
{no}
xr_fx
(x+ 'r ){x * P}
6734
?387
8010
8698
13. 25x? * Bl
\-*}- :l&
lZ Zxz+?r-9
11" $r+2s*B
x{x*T}
{,
d\
,J
(o)&)
T}
*15,S xr+ql?,ffix + ry-#ry*'?
U=
3
*
y * intercept {ansr,ler only}:
ga. Use your W*pBrtg calculator to find a quadratic model for the attendance at
men's college basketball games starting fu 1960 {year 0).
gb.
(-t, s)
L
*a= (-t)e+P{-t}+
intercept (ansrryer onlY):
ur
,
(s*)** fq)*
(s x *E){g )4 *,q)
Jxorlx"-3x-t t,* 3
x(eK+q)*r(**+q)
{n-,}{*K#q}
S'actor and solve each qnadratic equation.
L4.
l**LLx+B-ff
PL{
d*Y
\-*--lt
*rL'*?
3x?*t;,x -?j-]1$xs
--
3
-,#
x(x-q) * 3{x *'#}
x*
(;v.-s)(r*Y)*#
tx\*3=# X*Y;0
f,=#e
XsL'f
ls, f+8x+ld=o
U+L{Xxoq):
(x +'{}e : g
'Xtt5r"
x5
*t
L6.
A
*-9=0
( x* 3) {x*3} = o
X* 3;c> pe,k3 s #
Mx.g
M
s'*3
A-'= *
Simplify each expre$sion.
tli
(-;r#+i iur**i); {u
*3) d* **f
J
t\ a.+ ryi
*/
,* ruf "*
{*/+ ?.*-i;
r'
-i-f,l{r,b
5;*
JLffi
f"iJt
2r. (5 -
- 2')
+ Sa
(?
j + Uu* !
19. (-i + 1).9:_=
ry
uJ-'q
20. (3 + 4') -
f,\
$.d:nx's')
-r20
17.
f
22.
+ 6')
'Xe
&tS+3*x-*$o.
=-gu;#
,e"h
O
,-?
f,
"s *\
L*s
t
C-*
{3 + 8f) + {s * 2t}
B
+&;
gd+#fr
Find the additive inverse of each number.
23.
2-i
*J+'L
-(r*;).r
21.
+3i
ei. \
bi"-lit'*ixJs
-1
l-J*?
t
{ *rrL.
ZS. Fintt the absolute yalue of the complex numbers. Graph the Point
b' -4+8i
a. 7*2i
It-).1
{:}'+ {*s}
=
Imaginary
n
Imaginary
\*t{ t B*tr=
[ r- '*
r" ,#_b
J
Real
Real
.lp
$olve by nsing the Quadratic Formula
26. 3#+1x-10=0
dq)
l,x a r-;T--
-.*
fl= ,
1.
3 re*w
w
#{3}
\/ Y #
\
q
ffi{",;
t* + i*ff;ry
*f 'T'4
-p
E
.d'
\d &
.(&
w
*L$l*"\ J
was&ns,w*Rlgffi
&"
i
#{3}
3*tr
.--ffi
f3Xt {{J,
x=
*"
*+3x*5=0
glEeJ*It14ldh{trdili**s'de
aq a
F*.*
27.
f#
\d* rs S ,q. rj*fE
#&
Mxddnrru *
'a
/P R
b
iI@
4d64ef
$#+m*i#*tffit
r*E*
waese*s
-'u-#TT
d#i
da*sd&ffidffi
s"s,
@h
#
ffir
Evaluate the distriminant of each equntion. How milny rcal and/or imaginary solutions does each have?
29. 3x2-x*3:0
28" x?+6x-?=*
ielLH{}}{*T}
; {t-^l
4!*i
ffi tu-f
f*t)'-ry {s}fs} l
d
-3$
c
5af
"dr***u*r
*2
t
rw
*f, *
o,
y
g a /*"$ r *x
.6
*$
/a**
3+8^_*S*#r*
'lS * ?t* *&d*/)
r{{ *}i* + tu
*{f + {";
/{-**
F
\ .",\L /(rx&*8x+1=g
/ \ a" )
L--\n 31.
Solve by completing the square.
*+6x*1=a
30.
x* +bx+t
r TtS
Llrr-) -1
{ N+J}} # /.#
H*S ri,ff;
e*d@#
H;:*SSY f'
r
32.
M
/b { x#* t/px *jh,) s
(
f (-,tr,{r)
/*{ xGyry} #m "*J
dx-,t/*3** *V,
H.tr
$
riF
,l + fb{t{tub
u
,-xfr
x*'/i = *r[H f
$
Htr*-!'t
*E x
l= a(-y,11
=
=!-L -1,9
0.1
g1 stc*.jg
(t) = -
a8t
V,9 t'+
rlffi
#(*#J
!ro
cd
*?
r
For a model rocket, the altitude /l, in meters, as a function of time r, in seconds, is give by L = 68r
(a) Howmuchtimedoasittaketoreachthemaximumheight? h
*
.,1,
tt ffs&
-
4.9F.
(b) Find the maximum height of the rocket.
/ (t,1r1):
-/,?(r,,qsq)d +ds fu'q sq) = J3s' 1r8 m'l'r t
33. A lighting fixture manufacturer
has daily production costs
of C = A .25n2
- l\n
+ 800 , where C is the total daily cost in
dollars and r is the number of light fixnnes produced.
(a) How many fixtures should be produced to yield a minimum cost?
{fit *
# t"{*,rn\
F
/#
f,L} t ...d, {\as
rl
ffim*nd#* @s
. *-* ;
@
# f,}
** {n}q\
6ld \{J"d*r
O)
f
{:#
*..*"1 *.-
#*S
i
I
C*r-r d J
What is the minimum cost?
C, o,?S{co}r*to{ro}*rdcl z
34. Find
a quadratic function that includes the values in the
quadratictunction.
?aO Jotlo' t
able.
Show your system of equations, your matrices, and the final
l(n-b +c =t a)
,(a-L+E a r))
l3:a(-r), + L(-r)+C
Tq+ib+c:1
ta+pla+c;3
3:a(e)r"tb{e}tt
l--a(:)'+ atri n r,/ ;*-af*ps:?y 3a-3\+3c=3b
W^n'1"
5
t-3l-4 I'
/
*+
\, r,tffi a*!*c*r,
,
/'
a*b+C,:,) //
* }r\
?.nL{
t!a+Bb+Cs 3;r
$*
'* *3*
Lt
i
Lc+3111=fi .r)(.-^-\
bur calculator.
ru
fxi*5x*V*S
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l,oB
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_TryT-.,.."1,
xd-*s,{"!*{
x
Eat*
l?o+{c:1o
Z;r;rT
b:-L*
Sketch ysur graph ta the right.
X
avb+e
Ia+/'+c=1
-l
\'-\
sJ
35. Solve the quadratie *qnffitton by grapld
s* -5x* 4
r'ia+/b+C =J.
qi"d-t*:t*
-*T*+3e s)1
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9.
t,l.i.'i'ff..,j,lili..i,l:-i
',,,', :,,, ;,, sl-,, t,,i,,, I,',,,
:'.; .i; -1", i..',,.:-+A1.,:.'.',.,".' , : ',.:.: