7.
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1
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!x ! [7 " 8 " 10 "2(11) " 12 " 2(13) " 2(14) "
2(15) " 2(16) " 2(17) " 2(19) " 2(20) "
3(21) " 2(22) " 3(23) " 24 " 25] # 30
! 512 # 30
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(7 $ 17.07)2 " (8 $ 17.07)2 "
(10 $ 17.07)2 "2(11 $ 17.07)2 " (12 $ 17.07)2 "
2(13 $ 17.07)2 " 2(14 $ 17.07)2 " 2(15 $ 17.07)2 "
2(16 $ 17.07)2 " 2(17 $ 17.07)2 " 2 (19 $ 17.07)2 "
2(20 $ 17.07)2 " 2(21 $ 17.07)2 " 2(22 $ 17.07)2 "
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" 4.89
Page 891 Lesson 6-9
2 !!(y
2
6. d ! %(x
!!2 $
!!x!
!!2 $
!!y!
1)!"
1)
1.
7.5 $ 0.5 ! 7
7.5 " 0.5 ! 8
7.5 $ 2(0.5) ! 6.5
7.5 " 2(0.5) ! 8.5
7.5 $ 3(0.5) ! 6
7.5 " 3(0.5) ! 9
1a. 34 " 34 ! 68; 68%
1b. 34%
1c. 13.5 " 34 " 34 " 13.5 " 2 " 0.5 ! 97.5; 97.5%
1d. 2 " 13.5 " 34 " 34 " 13.5 ! 97; 97%
100 & 0.97 ! 97
2.
22 $ 7.5 ! 14.5
22 " 7.5 ! 29.5
22 $ 2(7.5) ! 7
22 " 2(7.5) ! 37
22 $ 3(7.5) ! $0.5
22 " 3(7.5) ! 44.5
2a. 34 " 13.5 " 2 " 0.5 ! 50;
50%; 3000 & 0.50 ! 1500
2b. 13.5 " 34 " 34 ! 81.5; 81.5%;
3000 & 0.815 ! 2445
2c. 2 " 0.5 ! 2.5; 2.5%
3.
510 $ 80 ! 430
510 " 80 ! 590
510 $ 2(80) ! 350
510 " 2(80) ! 670
510 $ 3(80) ! 270
510 " 3(80) ! 750
3a. 34 " 13.5 " 2 " 0.5 ! 50; 50%;
50,000 & 0.50 ! 25,000
3b. 34 " 34 !68; 68%; 50,000 & 0.68 ! 34,000
3c. 13.5 " 34 " 34 " 13.5 " 2 " 0.5 ! 97.5; 97.5%
3d. 0.5%
! %[5
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$!($
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x1 " x2
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7 " ($11) $3 " 13
, % ' ! & %%
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x1 " x2 y1 " y2
%, %
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2
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! (4.5, 15.5)
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43 " ($78) $18 " ($32)
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$35 $50
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! &%2%, %2%'
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11.
Page 892 Lesson 7- 1
2 !!(y
2
1. d ! %(x
!!2 $
!!x!
!!2 $
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1)!"
1)!
$8 " 0.34 4.19 " 20
, %% '
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$7.66 24.19
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16 " ($7) 29 " 2
, %'
' ! & %%
2
2
1
! &%9%, %3%
2 2 '
684 " 528 $239 " ($735)
, %% '
' ! & %%
2
2
1212 $974
! &%
%, %%'
2
2
! (606, $487)
447
Algebra 2 Extra Practice
13.
d ! !(x
""2 "
""x"
)2"#
""(y""2 "
""y"
)2"
1
1
25 ! !(p
""
""
8"
)2"
#"(3
""
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27
""
)2
2
625 ! (p " 8) # 576
49 ! (p " 8)2
$7 ! p " 8
$7 # 8 ! p
p!8#7
or
p!8"7
! 15
!1
14.
25 ! !("
"6".8
""
""
3.7
""
)2"
#"[p
""
""("
"8".9
")]"2"
2
625 ! 110.25 # (p # 8.9)
514.75 ! (p # 8.9)2
$22.69 # p # 8.9
"8.9 $ 22.69 # p
p # "8.9 # 22.69
or
p # "8.9 " 22.69
# 13.79
# "31.59
d ! !(x
"2""
""x"
)2"#
""(y"2""
""y"
)2"
1
1
25 ! ![p
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""("
"3"5")]"2"
625 ! (p # 29)2 # 49
576 ! (p # 29)2
$24 ! p # 29
"29 $ 24 ! p
p ! "29 # 24
or
p ! "29 " 24
! "5
! "53
2 ""(y
2
d ! !(x
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1)"#
1)"
21.
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2
625 ! (15 " p)
$25 ! 15 " p
"15 $ 25 ! "p
15 $ 25 ! p
p ! 15 # 25
or
p ! 15 " 25
! 40
! "10
16.
22.
2 ""(y
2
d ! !(x
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1)"#
1)
2!
23.
x1 # x2
"8.9 # x
%%
2
(x, y) !
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625 ! (p " 25)2 # 841
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no real solution
13)2
448
"16 # y
%%
2
4 ! "16 # y
20 ! y
y1 # y2
and
14.6 ! "8.9 # x
23.5 ! x
A (23.5, 9)
2 ""(y
2
d ! !(x
"2""
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"2""
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1)"#
1)"
© Glencoe/McGraw-Hill
and
, %%
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2
2
"8.9 # x "3.4 # y
(7.3, 2.8) ! $ %%
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(x, y) !
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25 ! ![8
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625 ! 121 # (p # 5)
504 ! (p # 5)2
$22.45 # p # 5
"5 $ 22.45 # p
p # "5 # 22.45
or
p # "5 " 22.45
# 17.45
# "27.45
18.
y1 # y2
x1 # x2
, %%
$%
2
2
5 # x "16 # y
("13, 2) ! $ % , %% %
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(x, y) !
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25 ! !("
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2
625 ! 576 # ("7 " p)
49 ! ("7 " p)2
$7 ! "7 " p
7 $ 7 ! "p
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p ! "7 # 7
or
p ! "7 " 7
!0
! "14
17.
d ! !(x
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1
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25 ! ![5
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625 ! 49 # (p " 6)2
576 ! (p " 6)2
$24 ! p " 6
6 $ 24 ! p
p ! 6 # 24
or
p ! 6 " 24
! 30
! "18
15.
d ! !(x
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1
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19.
$
!
x1 # x2
$
2
%% # x
3
%,
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# 8x
! 8x
5.6 ! "3.4 # y
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y1 # y2
5
%% # y
4
%
2
and
%
7
%%
12
!
5
%% # y
4
%
2
14 ! 15 # 12y
"1 ! 12y
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7
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12
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%%
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2
2
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3
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2
6
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3
2.8 !
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"%1%
12
12
Algebra 2 Extra Practice
Page 892 Lesson 7-2
1. y #
3
%%
4
y
! x2
! x2
$
vertex: 0,
5. y ! 2x2 " 8x # 7
y ! 2(x2 " 4x) # 7
y ! 2(x2 " 4x # 4) # 7 " 2(4)
y ! 2(x " 2)2 " 1
vertex: (2, "1)
axis of symmetry: x ! 2
y
y " 34 ! x 2
" %3%
4
"%3%
4
%
axis of symmetry: x ! 0
$
$
4(1) %
$
x
O
"%3%
4
directrix: y !
1
%%
4(1)
"
2%
or "1
$
% $
! (x " 2)2
%
1
1
% or "2, %%
focus: "2, 0 # %
4(5)
20
O
directrix: y ! 0 " %1% or "%1%
4(20)
$
focus: "1 #
x
20
y
4
! %3%(x
4
4(y " 2) ! 3(x # 1)2
O
vertex: (1, "2)
axis of symmetry: x ! 1
$
focus: 1, "2 #
$
1, "1%2%
3
%
$ %%
1
%
3
4 %%
4
directrix: y ! "2 "
3
%%(x
5
x
or
4
%%
3
$
$ %
directrix: x ! 3 "
%
5x " 3y 2 ! 15
O
$
1
%
3
4 "%%
5
$ %
x
$
%
© Glencoe/McGraw-Hill
$%
%
3(x # 8)2 ! 5(y " 3)
O
4
8
12
x
"4
or
1
%
3
4 %%
5
$%
or "3%5%
12
% $
&&
1
%
3
%%
5
or
5
%%
3
units
y
O
or
5
%%
3
1
%%
4(3)
or
2
11
%%
12
direction of opening: right,
since a & 0
length of the latus rectum:
direction of opening: left, since a ' 0
& &
4(3)
directrix: x ! 1 "
12
1
%
"3
%%
5
4
y
x ! 3(y " 4)2 " 1
x
%
focus: 1 # %1%, "4 or 1%1%, "4
or 3%5%
length of the latus rectum:
8
8. x ! 3(y # 4)2 # 1
vertex: (1, "4)
axis of symmetry: y ! "4
0 or 2%7%, 0
12
2
12
length of the latus rectum:
y
vertex: (3, 0)
axis of symmetry: y ! 0
1
%
3 ,
4 "%%
5
%
direction of opening: upward, since a & 0
units
5
focus: 3 #
1
%
3
4 %%
5
directrix: y ! "3 "
direction of opening: upward, since a & 0
4. 5x # 3y2 ! 15
5x ! "3y2 # 15
x ! "%3%y2 # 3
"1%1%
8
or
x
$8, "2%17%2 %
3
&&
1
%%
4(2)
vertex: (8, "3)
axis of symmetry: x ! 8
or "2%1%
1
%
3
%%
4
2
2 or
x ! 2y 2 # 8y " 7
O
% $
"%7%,
8
5
$
length of the latus rectum:
y
" 8)2 " 3 ! y
focus: 8, "3 #
$%
2
3(x " 8)2 ! 5(y # 3)
3
2
%%(x " 8) ! y # 3
7.
or
1
%
3
4 %%
4
8
&2&
y
" 1)2 " 2
or "1%1%
direction of opening: right, since a & 0
length of the latus rectum: %1% or %1% unit
5
3. 4(y # 2) ! 3(x " 1)2
y # 2 ! %3%(x " 1)2
1
%%,
4(2)
directrix: x ! "1 "
direction of opening: upward, since a & 0
length of the latus rectum: %1% or %1% units
&5&
%
6. x ! 2y2 " 8y # 7
x ! 2(y2 " 4y) # 7
x ! 2(y2 " 4y # 4) # 7 " 2(4)
x ! 2(y " 2)2 " 1
vertex: ("1, 2)
axis of symmetry: y ! 2
y
y
5
8
&2&
2)2
! (x #
y ! 5(x # 2)2
vertex: ("2, 0)
axis of symmetry: x ! "2
1
%%
4(2)
x
O
direction of opening: upward, since a & 0
length of the latus rectum: %1% or %1% unit
&1 &
2.
4(2)
directrix: y ! "1 "
direction of opening: upward, since a & 0
length of the latus rectum: %1% or 1 units
y
%%
5
y ! 2x 2 # 8x " 7
focus: 2, "1 # %1% or 2, "%7%
focus: 0, "%3% # %1% or 0, "%1%
4
% $
y
&%13%& or %13% unit
units
449
Algebra 2 Extra Practice
9. 8y # 5x2 # 15x # 9 ! 0
8y # 9 ! "5x2 " 15x
8y # 9 ! "5(x2 # 3x)
8y # 9 ! "5 x2 # 3x # %9% # 5
12. "8y ! x2
y ! "%1%x2
8
vertex: (0, 0)
axis of symmetry: x ! 0
$
$%94%%
4%
2
5
8y # 9 ! "5$x # %3%% # %4%
2
4
2
5
8y ! "5$x # %3%% # %4%
"9
2
4
2
8y ! "5$x # %3%% # %9%
2
4
2
y ! "%5%$x # %3%% # %9%
8
2
32
y
vertex: $"%3%, %9%%
2 32
8y " 5x " 15x " 9 ! 0
$
focus: 0, 0 #
$
9
%%
2 32
focus: "%3%,
$
"%3%,
2
#
%
directrix: y !
1
%
5
4 "%%
8
or
$
9
"%1%
160
9
%%
32
%%
or
1
%
5
4 "%%
8
"
$ %
13.
109
%%
160
& &
1
%
5
"%%
8
or
8
%%
5
vertex:
$
9
"%1%
,
5
"
%
"12 "8 "4 O
"4
4
focus:
$
9
"%1%
5
#
9
directrix: x ! "%1%
"
5
%
4 or
$ %
1
%
1
4 "%%
5
$ %
$
101
"%
%,
20
11. 6x ! y2 " 6y # 39
6x ! (y2 " 6y # 9) # 39 " 9
x ! %16%(y " 3)2 # 5
x
$
%
4
1
%
1
"%%
5
$
focus: 5 #
$%
directrix: x ! 5 "
%
$
1
%
1
4 %%
6
$%
&%14%& or %14% unit
% $
48
y
32
y ! x 2 # 6x " 33
16
O
%
"24 "8
8
24
40 x
or 5 units
"4 O
"4
4
8
&%11%& or 1 unit
15. y ! x2 # 4x # 1
y ! (x2 # 4x # 4) # 1 " 4
y ! (x # 2)2 " 3
vertex: ("2, "3)
axis of symmetry: x ! "2
y
O
$
4(1) %
3
$"2, "2%4%%
focus: "2, "3 # %1% or
4
%
16
length of the latus rectum:
12
6x ! y 2 # 6y " 39
8
2
or "2%1%
direction of opening: upward, since a & 0
y
3 or 6%1%, 3
x
1
3
% or 23%%
directrix: y ! 24 " %
4(1)
4
20
& &
O
(x " 3) 2 ! 14 (y # 2)
1
1
% or 3, 24%%
focus: 3, 24 # %
4(1)
4
or "%51%
vertex: (5, 3)
axis of symmetry: y ! 3
1
%
1 ,
4 %%
6
or 8 units
y
14. y ! x2 " 6x # 33
y ! (x2 " 6x # 9) # 33 " 9
y ! (x " 3)2 # 24
vertex: (3, 24)
axis of symmetry: x ! 3
direction of opening: left, since a ' 0
length of the latus rectum:
1
%
4(4)
length of the latus rectum:
x ! # 15 y 2 " 85 y # 7
19
%%
5
1
%
1 ,
4 "%%
5
& &
1
%
1
"%%
8
direction of opening: upward, since a & 0
y
8
axis of symmetry: y ! 4
or 2
(x # 3)2 ! %14%(y # 2)
directrix: y ! "2 "
12
x ! "%15%(y2 " 8y # 16) " 7 # %15%(16)
"
$ %
$
4(4) %
15
$"3, "1%1%6 %
units
x ! "%15%(y2 " 8y) " 7
x
1
%
1
4 "%%
8
4(x # 3) ! y # 2
4(x # 3)2 " 2 ! y
vertex: ("3, "2)
axis of symmetry: x ! "3
1
focus: "3, "2 # %
or
5
4)2
or (0, "2)
2
10. x ! "%15%y2 # %8%y " 7
! "%15%(y
%
#8y ! x 2
length of the latus rectum:
direction of opening: downward, since a ' 0
length of the latus rectum:
$ %
x
O
direction of opening: downward, since a ' 0
x
O
2
1
%
1
4 "%%
8
directrix: y ! 0 "
2
axis of symmetry: x ! "%3%
y
x
y ! x 2 " 4x " 1
directrix: y ! "3 " %1% or "3%1%
12 x
4(1)
4
direction of opening: upward, since a & 0
length of the latus rectum:
or 3%1%
&%11%& or 1 unit
2
direction of opening: right, since a & 0
length of the latus rectum:
© Glencoe/McGraw-Hill
&&
1
%
1
%%
6
or 6 units
450
Algebra 2 Extra Practice
16. 4(x " 2) ! (y # 3)2
x " 2 ! %1%(y # 3)2
x!
4
1
%%(y
4
O
$
directrix: x
x
2
# 3) # 2
2
4(x # 2) ! (y " 3)
vertex: (2, "3)
axis of symmetry: y ! "3
focus: 2 #
(x " h)2 # (y " k)2 ! r2
(x " !2
")2 # (y " 4)2 ! 92
(x " !2
")2 # (y " 4)2 ! 81
6.
(x " h)2 # (y " k)2 ! r2
[x " ("8)]2 # [y " ("!1
"0
")]2 ! 112
2
(x # 8) # (y # !1
"0
")2 ! 121
2
2
7.
(x " h) # (y " k) ! r2
(x " 0.8)2 # (y " 0.5)2 ! (0.2)2
(x " 0.8)2 # (y " 0.5)2 ! 0.04
8.
(x " h)2 # (y " k)2 ! r2
2
[x " ("9)]2 # (y " 0)2 ! %57%
5.
y
%
1
%
1 , "3 or (3, "3)
4 %%
4
1
%
! 2 " 1 or 1
4 %%
4
$%
$%
$%
direction of opening: right, since a & 0
length of the latus rectum:
(y " 8)2 ! "4(x " 4)
" 8)2 ! x " 4
17.
&&
1
%
1
%%
4
y
24
(y # 8)2 ! #4(x # 4)
16
"%1%(y " 8)2 # 4 ! x
8
4
vertex: (4, 8)
axis of symmetry: y ! 8
$
focus: 4 #
$ %
directrix: x ! 4 "
"24 "16 "8 O
O (0, 0)
%
or 5
$ %
11. (x " 5)2 # (y # 4)2 ! 1
center: (5, "4)
radius: !1
" or 1 unit
& &
1
%
1
"%%
4
(x #
%
$%
4)2
or
1
%
1
4 %%
6
$%
5
5
x2 # 3x # %94% # y2 " 5y # %24%
! %12% # %94% " %24%
3
%%
2
2
$x # %32%%
center: $"%32%, %52%%
or "%3%
2
&&
x2 # 3x # y2 " 5y ! %12%
12.
$ , "2%
1
%
1
%%
6
radius:
35
%%
4
%
2
5
! %34%
y
!3
"5
"
%
2
units
(# 32 , 52 )
O
x 2 " 3x " y 2 # 5y ! 12
1. (x " h)2 # (y " k)2 ! r2
(x " 3)2 # (y " 2)2 ! 52
(x " 3)2 # (y " 2)2 ! 25
2.
(x " h)2 # (y " k)2 ! r2
[x " ("5)]2 # (y " 8)2 ! 32
(x # 5)2 # (y " 8)2 ! 9
3.
(x " h)2 # (y " k)2 ! r2
2
(x " 1)2 # [y " ("6)]2 ! $%23%%
!
13.
x
x2 # y2 ! 14x " 24
" 14x # y2 ! "24
2
x " 14x # 49 # y2 ! "24 # 49
(x " 7)2 # y2 ! 25
y
8
x 2 " y 2 ! 14x # 24
center: (7, 0)
radius: !2
"5
" or 5 units
4
x2
(7, 0)
4
%%
9
O
4. (x " h)2 # (y " k)2 ! r2
(x " 0)2 # (y " 7)2 ! (!6
")2
2
2
x # (y " 7) ! 6
© Glencoe/McGraw-Hill
'(( or
$
# y " %52%
or 6 units
Page 892 Lesson 7–3
6)2
!1
x
6x ! y 2 " 4y " 4
length of the latus rectum:
# (y #
5)2 " (y "
(5, #4)
direction of opening: right, since a & 0
(x "
x
O
or 4 units
O
vertex: (0, "2)
axis of symmetry: y ! "2
1)2
y
y
1
%
1 , "2
4 %%
6
8x
4
"8 "4
"4
"8
1
%
1
4 "%%
4
18. 6x ! y2 # 4y # 4
x ! %16%(y # 2)2
directrix: x ! 0 "
4
8 or (3, 8)
length of the latus rectum:
$
y
8 x 2 " y 2 ! 36
8x
direction of opening: left, since a ' 0
focus: 0 #
2
9. (x " h)2 # (y " k)2 ! r2
(x " 4)2 # (y " 1)2 ! 42
(x " 4)2 # (y " 1)2 ! 16
10. x2 # y2 ! 36
center: (0, 0)
radius: !3
"6
" or 6 units
or 4 units
"%1%(y
4
1
%
1 ,
4 "%%
4
5
(x # 9) # y ! %24%
9
2
4
8
12 x
"4
"8
451
Algebra 2 Extra Practice
14.
x2 # y2 ! 2(y " x)
x2 # y2 ! 2y " 2x
x2 # 2x # y2 " 2y ! 0
x2 # 2x # 1 # y2 " 2y # 1 ! 1 # 1
(x # 1)2 # (y " 1)2 ! 2
center: ("1, 1)
radius: !2
" units
19.
y
x2 # y2 " 2 (!5
"x " !7
"y) ! 1
x2 " 2 !5
"x # y2 # 2 !7
"y ! 1
x2 " 2 !5
"x # 5 # y2 # 2 !7
"y # 7 ! 1 # 5 # 7
(x " !5
")2 # (y # !7
")2 ! 13
center: (!5
", "!7
")
y
x 2 " y 2 # 2(!)5x #!)
7y ) ! 1
radius: !1
"3
" units
x 2 " y 2 ! 2(y # x)
x
O
(#1, 1)
15.
(!)5, !)7)
x
O
20. 16 (x2 # y2) " 8 (3x # 5y) # 33 ! 0
3
x2 # y2 " %1%(3x # 5y) # %31%
!0
6
x2 # 10x # (y " !3
")2 ! 11
2
x # 10x # 25 # (y " !3
")2 ! 11 # 25
2
(x # 5) # (y " !3
")2 ! 36
center: ("5, !3
")
y
x 2 " 5x " (y # !)3)2 ! 11
radius: !3
"6
" or 6 units
8
2
3
x2 " %32%x # y2 " %52%y ! "%31%
6
5
3
5
x2 " %32%x # %9% # y2 " %52%y # %21%
! "%31%
# %19%
# %21%
6
6
6
6
16
$
3 5
center: $%4%, %4%%
(#5, !)3) 4
"12 "8 "4 O
"4
16.
x2
radius:
2
! %11%
6
1
%%
4
units
( 34 , 54 )
3
2
1
16(x 2 " y 2) # 8(3x " 5y) " 33 ! 0
O
1
2
x
3
2
1
(2, 0)
Page 893 Lesson 7-4
x
O
1.
x2 # y2 # 12x " 10y # 45 ! 0
# 12x # 36 # y2 " 10y # 25 ! "45 # 36 # 25
(x # 6)2 # (y " 5)2 ! 16
center: ("6, 5)
y
12
radius: !1
"6
" or 4 units
2
2
x " y " 12x # 10y " 45 ! 0
8
4
"12 "8 "4 O
"4
2.
4x
2
# %y% ! 1
81
8
x2
%
121
#
(y " 5)2
%
16
!1
20
y
x2
36
"
4
y2
81
!1
8x
y
center: (0, 5)
(0, 5)
10
a ! 11, b ! 4
b2 ! a2 " c2
"20 "10 O
10 20 x
16 ! 121 " c2
"10
c2 ! 105
2
x2
" (y " 5) ! 1
121
16
c ! !1
"0
"5
"
foci: (0 $ !1
"0
"5
", 5)
length of major axis: 2(11) or 22
length of minor axis: 2(4) or 8
x2 # y2 " 6x # 4y ! 156
x2 " 6x # y2 # 4y ! 156
x2 " 6x # 9 # y2 # 4y # 4 ! 156 # 9 # 4
(x " 3)2 # (y # 2)2 ! 169
center: (3, "2)
y
radius: !1
"6
"9
" or 13 units
6
"6 O
6
12
"6 (3, #2)
x2
%%
36
center: (0, 0)
4
a ! 9, b ! 6
(0, 0)
b2 ! a2 " c2
"8 "4
36 ! 81 " c2
"4
c2 ! 45
c ! 3!5
"
"8
foci (0, $3!5
"
length of major axis: 2(9) or 18
length of minor axis: 2(6) or 12
x2
(#6, 5)
18.
1
%%
16
%
y
y
x 2 " y 2 ! 4x " 9
17.
'(( or
$
# y " %54%
1
2
y2
# ! 4x # 9
x2 " 4x # y2 ! 9
x2 " 4x # 4 # y2 ! 9 # 4
(x " 2)2 # y2 ! 13
center: (2, 0)
radius: !1
"3
" units
4x
2
%
x " %34%
x
"12
x 2 " y 2 # 6x " 4y ! 156
© Glencoe/McGraw-Hill
452
Algebra 2 Extra Practice
3.
(x # 2)2
%
12
#
(y # 1)2
%
16
!1
8.
y
center: ("2, "1)
(x " 2)
" (y " 1) ! 1
12
16
a ! 4, b ! !1
"2
" or 2!3
"
2
2
2
O
b !a "c
2
(#2,
#1)
12 ! 16 " c
c2 ! 4
c!2
foci: ("2, "1 $ 2) or
("2, "3), (2, 1)
length of major axis: 2(4) or 8
length of minor axis: 2(2!3
") or 4!3
"
2
4.
5)2
(x "
%
25
#
3)2
(y #
%
75
!1
y
2
x
9.
" (y " 3)
75
2
4
center: (5, "3)
a ! !7
"5
" or 5!3
", b ! 5
"4 O
b2 ! a2 " c2
8
4
"4
c2 ! 50
(5, #3)
25 ! 75 " c2
"8
c ! 5!2
"
foci: (5, "3 $ 5!2
")
length of major axis: 2(5!3
") or 10!3
"
length of minor axis: 2(5) or 10
5.
x2
%
9
#
y2
%
36
!1
y
8
x2
(x " 8)2
%
4
#
(y # 8)2
%
1
!1
4
center: (8, "8)
a ! 2, b ! 1
"4 O
b2 ! a2 " c2
"4
1 ! 4 " c2
"8
c2 ! 3
"12
c ! $!3
"
foci: (8 $ !3
", "8)
length of major axis: 2(2) or 4
length of minor axis: 2(1) or 2
7.
(x # 2)2
%
36
#
(y " 4)2
%
40
!1
!1
24
(x " 4)2
%
16
x2
%
4
2
" y !1
#
(y # 1)2
%
9
!1
8
#
y2
%
16
8x
x2
%
12
y
#
y2
%
28
(x # 8) 2 (y " 8) 2
"
!1
4
1
y
y
!1
4
12. 9x2 # 16y2 ! 144
x2
%
16
#
y2
%
9
453
8x
y
9x 2 " 16y 2 ! 144
!1
center: (0, 0)
a ! 4, b ! 3
b2 ! a2 " c2
9 ! 16 " c2
c2 ! 7
c ! !7
"
foci: (!7
", 0) and ("!7
", 0)
length of major axis: 2(4) or 8
length of minor axis: 2(3) or 6
x
x
8
7x 2 " 3y 2 ! 84
center: (0, 0)
(0, 0)
"8
" or 2!7
",
a ! !2
O
"8 "4
4
b ! !1
"2
" or 2!3
"
"4
b2 ! a2 " c2
"8
12 ! 28 " c2
2
c ! 16
c!4
foci: (0, 4) and (0, "4)
length of major axis: 2(2!7
") or 4!7
"
length of minor axis: 2(2!3
") or 4!3
"
12x
(8, #8)
12
y
!1
11. 7x2 # 3y2 ! 84
8
8x
center: (0, 0)
(0, 0)
a ! 4, b ! 2
O
b2 ! a2 " c2
8x 2 " 2y 2 ! 32
4 ! 16 " c2
c2 ! 12
c ! 2!3
"
foci: (0, $2!3
"
length of major axis: 2(4) or 8
length of minor axis: 2(2) or 4
36
y
4
y
(x " 8) 2 (y # 7) 2
"
!1
121
64
10. 8x2 # 2y2 ! 32
center: ("2, 4)
(x " 2) 2 (y # 4) 2
"
!1
a ! !4
"0
" or 2!1
"0
", b ! 6
36
40
2
2
2
b !a "c
(#2, 4)
36 ! 40 " c2
2
"8 "4 O
4
c !4
"4
c!2
foci: ("2, 4 $ 2) or
("2, 2), ("2, 6)
length of major axis: 2(2!1
"0
") or 4!1
"0
"
length of minor axis: 2(6) or 12
© Glencoe/McGraw-Hill
(y " 7)2
%
64
2
2
center: (4, "1)
(x # 4)
" (y " 1) ! 1
4
16
9
a ! 4, b ! 3
b2 ! a2 " c2
12x
"4 O (4, #1) 8
9 ! 16 " c2
"4
c2 ! 7
"8
c ! !7
"
foci: (4 $ !7
", " 1)
length of major axis: 2(4) or 8
length of minor axis: 2(3) or 6
!1
12 x
9
center: (0, 0)
4
a ! 6, b ! 3
(0, 0)
b2 ! a2 " c2
O
"8 "4
4
9 ! 36 " c2
"4
2
c ! 27
"8
c ! 3!3
"
foci: (0, $3!3
")
length of major axis: 2(6) or 12
length of minor axis: 2(3) or 6
6.
#
center: ("8, 7)
16
a ! 11, b ! 8
(#8, 7)
2
2
2
b !a "c
8
64 ! 121 " c2
c2 ! 57
#24 #16 #8 O
#8
c ! !5
"7
"
foci: ("8 $ !5
"7
", 7)
length of major axis: 2(11) or 22
length of minor axis: 2(8) or 16
2
(x # 5)
25
(x # 8)2
%
121
O (0, 0)
x
Algebra 2 Extra Practice
13. 169x2 " 338x # 169 # 25y2 ! 4225
169(x2 " 2x # 1) # 25y2 ! 4225
169(x " 1)2 # 25y2 ! 4225
(x " 1)2
y2
% # % !1
25
17.
169
(x " 1)2
%
12
center: (1, 0)
y
12
a ! 13, b ! 5
b2 ! a2 " c2
6
(1, 0)
25 ! 169 " c2
c2 ! 144
"18 "12 "6 O
12 18x
6
c ! 12
"6
169x 2 # 338x " 169 " 25y 2 ! 4225
foci: (1, 12) and
"12
(1, "12)
length of major axis: 2(13) or 26
length of minor axis: 2(5) or 10
14.
x2 # 4y2 # 8x " 64y # 236 ! 0
x2 # 8x # 4y2 " 64y ! "236
x2 # 8x # 16 # 4(y2 " 16y # 64) ! "236 # 16 # 256
(x # 4)2 # 4(y " 8)2 ! 36
(x # 4)2
(y " 8)2
% # % !1
36
9
(x # 3)2
%
9
(y # 4)2
%
24
!1
#
(y " 5)2
%
4
!1
center: ("3, 5)
y
a ! 3, b ! 2
b2 ! a2 " c2
(#3, 5)
4 ! 9 " c2
2
2
2
4x " 9y " 24x # 90y ! #225
c !5
c ! !5
"
foci: ("3 $ !5
", 5)
x
O
length of major axis:
2(3) or 6
length of minor axis: 2(2) or 4
19.
9x2 # 10y2 # 54x # 20y ! "1
9x2 # 54x # 10y2 # 20y ! "1
2
9(x # 6x # 9) # 10(y2 # 2y # 1) ! "1 # 81 # 1
9(x # 3)2 # 10(y # 1)2 ! 81
(x # 3)2
%
9
100
center: (3, 2)
y
4x 2 " 5y 2 ! 4(6x " 5y " 111)
a ! !1
"2
"5
" or 5!5
", b ! 10
12
b2 ! a2 " c2
6 (3, 2)
100 ! 25 " c2
c2 ! 25
"6 O
6 12 x
c!5
"6
foci: (3 $ 5, 2) or
(8, 2), ("2, 2)
length of major axis: 2(5!5
") or 10!5
"
length of minor axis: 2(10) or 20
16.
169x2 # y2 # 2366x ! 4y " 8116
169x2 # 2366x # y2 " 4y ! "8116
169(x2 #14x#49)#(y2 "4y#4)! "8116#8281#4
169(x # 7)2 # (y " 2)2 ! 169
(x # 7)2
(y " 2)2
% # % !1
1
#
center: (1, "4)
y
6
"4
" or 2!6
",
a ! !2
b ! !1
"2
" or 2!3
"
"12 "6 O
6 12x
b2 ! a2 " c2
"6 (1, #4)
2
12 ! 24 " c
c2 ! 12
2x 2 " y 2 # 4x " 8y # 6 ! 0
c ! 2!3
"
"18
foci: (1, "4 $ 2!3
"
length of major axis: 2(2!6
") or 4!6
"
length of minor axis: 2(2!3
") or 4!3
"
18.
4x2 # 9y2 # 24x " 90y ! "225
4x2 # 24x # 9y2 " 90y ! "225
4(x2 # 6x # 9) # 9(y2 " 10y # 25) ! "225 # 36 # 225
4(x # 3)2 # 9(y " 5)2 ! 36
center: ("4, 8)
y
a ! 6, b ! 3
12
b2 ! a2 " c2
(#4, 8)
8
9 ! 36 " c2
2
c ! 27
x 2 " 4y 2 " 8x # 64y " 236 ! 0
c ! 3!3
"
foci: ("4 $ 3!3
", 8)
"12 "8 "4 O
4 x
length of major axis:
2(6) or 12
length of minor axis: 2(3) or 6
15.
4x2 # 5y2 ! 4(6x # 5y # 111)
4x2 # 5y2 ! 24x # 20y # 444
4x2 " 24x # 5y2 " 20y ! 444
4(x2 " 6x # 9) # 5(y2 " 4y # 4) ! 444 # 36 # 20
4(x " 3)2 # 5(y " 2)2 ! 500
(x "3)2
(y " 2)2
% # % !1
125
2x2 # y2 " 4x # 8y " 6 ! 0
2x2 " 4x # y2 # 8y ! 6
2(x2 " 2x # 1) # (y2 # 8y # 16) ! 6 # 2 # 16
2(x " 1)2 # (y # 4)2 ! 24
#
center: ("3, "1)
a ! 3, b !
y
"12 "8 "4 O
(#3, #1) "4
c2 ! %119%
0
$
4
8x
"8
19!1
"0
"
%
10
foci: "3 $
!1
8
9x 2 " 10y 2 " 54x " 20y ! #1
4
9!1
"0
"
%
10
2
b2 ! a 2 " c
81
%% ! 9 " c2
10
c!
(y # 1)2
%
81
%%
10
19!1
"0
" 9!1
"0
"
%, %
10
10
%
length of major axis: 2(3) or 6
9!1
"0
"
9!1
"0
"
or %
$%
10 %
5
length of minor axis: 2
169
center: ("7, 2)
y
a ! 13, b ! 1
12
b2 ! a2 " c2
2
6
1 ! 169 " c
(#7, 2)
c2 ! 168
"24 "18 "12 "6 O
6 x
"2
"
c ! 2!4
foci: ("7, 2 $ 2!4
"2
")
2
2
169x " y " 2366x ! 4y # 8116
length of major axis:
2(13) or 26
length of minor axis: 2(1) or 2
© Glencoe/McGraw-Hill
454
Algebra 2 Extra Practice
20.
9x2 # 16y2 " 54x # 64y # 1 ! 0
9x2 " 54x # 16y2 # 64y ! "1
9(x2 " 6x # 9) # 16(y2 # 4y # 4) ! "1 # 81 # 64
9(x " 3)2 # 16(y # 2)2 ! 144
(x " 3)2
(y # 2)2
% # % !1
16
5.
9
6.
"
x2
%
9
!1
center: (0, 0)
a ! 5, b ! 3
vertices: (0, 5), (0, "5)
c2 ! a2 # b2
c2 ! 25 # 9
c2 ! 34
c ! !3
"4
"
foci: (0, !3
"4
"), (0, "!3
"4
")
slopes of asymptotes: $%53%
2.
x2
%
4
"
y2
%
9
x2
%
81
"
y2
%
36
!1
y
y2
4
x2
O 25 # 9 ! 1
"6 "2
2
6 x
"4
7.
"8
!1
center: (0, 0)
a ! 2, b ! 3
vertices: (2, 0), ("2, 0)
c2 ! a2 # b2
c2 ! 4 # 9
c2 ! 13
c ! !1
"3
"
foci: (!1
"3
", 0), ("!1
"3
", 0)
slopes of asymptotes: $%32%
3.
8
x
x2 y2
# !1
4
9
12
8.
x2
%
9
"
y2
%
16
!1
center: (0, 0)
a ! 3, b ! 4
vertices: (3, 0), ("3, 0)
c2 ! a2 # b2
c2 ! 9 # 16
c2 ! 25
c !5
foci: (5, 0), ("5, 0)
slopes of asymptotes: $%34%
y
© Glencoe/McGraw-Hill
x2
%
16
"
y2
%
4
!1
8
y
x2
y2
(x " 4)2
%
64
"
(y # 1)2
%
16
!1
y
16
(x # 4) 2 (y " 1) 2
#
!1
64 8
16
(y " 7)2
%
2.25
"
(x " 3)2
%
4
!1
8
16
x
(y # 7) 2 (x # 3) 2
#
!1
2.25 y
4
12
8
4
"4 O
4
8
x
9. (x # 5)2 " (y # 3)2 ! 1
(y " 3) 2
(x " 5) 2 #
!1
center: ("5, "3)
48 y
a ! 1, b ! 2
4
vertices: ("5 $ 1, "3) or
x
("6, "3), ("4, "3)
2
2
2
"12
"8
"4
4
O
c !a # b
"4
c2 ! 1 # 4
c2 ! 5
"8
c ! !5
"
foci: ("5 $ !5
", "3)
slopes of asymptotes: $%21%
y
O
y
16
center: (3, 7)
a ! 1.5, b ! 2
vertices: (3, 7 $ 1.5) or
(3, 8.5), (3, 5.5)
c2 ! a2 # b2
c2 ! 2.25 # 4
c2 ! 6.25
c ! 2.5
foci: (3, 7 $ 2.5) or
(3, 9.5), (3, 4.5)
1.5
%
slopes of asymptotes: $%
2
center: (0, 0)
6
a ! 9, b ! 6
vertices: (9, 0), ("9, 0)
c2 ! a2 # b2
"12 "6 O
6
12x
c2 ! 81 # 36
"6
c2 ! 117
2
2
"12 x # y ! 1
c ! !1
"1
"7
" or 3!1
"3
"
81 36
foci: (3!1
"3
", 0), ("3!1
"3
", 0)
slopes of asymptotes: $%96% or $%32%
4.
!1
center: (4, "1)
a ! 8, b ! 4
vertices: (4 $ 8, "1) or
("4, "1), (12, "1)
"8 O
c2 ! a2 # b2
"8
c2 ! 64 # 16
"16
c2 ! 80
c ! 4!5
"
foci: (4 $ 4!5
", "1)
slopes of asymptotes: $%48% or $%12%
y
O
x2
%
144
#
!1
center: (0, 0)
16
4
4
a ! 4, b ! 2
x
vertices: (4, 0), ("4, 0)
2
2
2
"8
"4
4
8
c !a # b
O
"4
c2 ! 16 # 4
c2 ! 20
"8
c ! 2!5
"
foci: (2!5
", 0), ("2!5
", 0)
slopes of asymptotes: $%24% or $%12%
Page 893 Lesson 7-5
y2
%
25
"
center: (0, 0)
x2
8 y2
a ! 10, b ! 12
#
!1
100 144 x
vertices: (0, 10), (0, "10)
c2 ! a2 # b2
"16 "8 O
8 16
"8
c2 ! 100 # 144
c2 ! 244
"16
c ! !2
"4
"4
" or 2!6
"1
"
foci: (0, 2!6
"1
"),
(0, "2!6
"1
")
0
slopes of asymptotes: $%11%
or $%56%
2
center: (3, "2)
y
a ! 4, b ! 3
b2 ! a2 " c2
x
O
9 ! 16 " c2
c2 ! 7
(3, #2)
c ! !7
"
foci: (3 $ !7
", "2)
9x 2 " 16 y 2 # 54x " 64y " 1 ! 0
length of major axis: 2(4) or 8
length of minor axis: 2(3) or 6
1.
y2
%
100
x
x2 y2
# !1
9 16
455
Algebra 2 Extra Practice
10. x2 " 9y2 ! 36
x2
y2
%" %
36
4
8
!1
x 2 # 9y 2 ! 36
4
center: (0, 0)
a ! 6, b ! 2
"8 "4 O
vertices: (6, 0), ("6, 0)
"4
c2 ! a2 # b2
2
c ! 36 # 4
"8
c2 ! 40
c ! 2!1
"0
"
foci: ($2!1
"0
", 0)
slopes of asymptotes: $%26% or $%13%
11. 4x2 " 9y2 ! 36
x2
%
9
"
y2
%
4
y2
%
49
y2
%
49
144x2
x
4x 2 # 9y 2 ! 36
8
49x 2 # 16y 2 ! 784
4
x
4
8
"8
2
x
4
"12 "8 "4 O
"4
"8
"
(x # 1)2
%
23.04
!1
16. 25(y # 5)2 " 20(x " 1)2 ! 500
"
(x " 1)2
%!
25
1
center: (1, "5)
y
"0
" or 2!5
", b ! 5
a ! !2
"8 "4 O
4
8 12x
vertices: (1, "5 $2!5
")
"4
c2 ! a2 # b2
25(y " 5) 2 # 20(x # 1) 2 ! 500
c2 ! 20 # 25
"8
c2 ! 45
"12
c ! 3!5
"
foci: (1, "5 $ 3!5
")
2!"
5
%
slopes of asymptotes: $%
5
# 1152x "
" 100y ! 1396
144(x2 # 8x # 16) " 25(y2 " 4y # 4) ! 1396 #
2304 " 100
144(x # 4)2 " 25(y " 2)2 ! 3600
!1
center: ("4, 2)
144x 2 " 1152x # 25y 2 # 100y ! 1396
y
16
a ! 5, b ! 12
vertices: ("4 $ 5, 2) or
8
(1, 2), ("9, 2)
c2 ! a2 # b2
"24 "16 "8 O
8
16 x
"8
c2 ! 25 # 144
c2 ! 169
"16
c ! 13
foci: ("4 $ 13, 2) or ("17, 2), (9, 2)
2
slopes of asymptotes: $%15%
© Glencoe/McGraw-Hill
y
8
576y ! 49x " 490x " 29,449
4
2
23.04y2 " 46.08y " 1.96x2 " 3.92x ! 24.0784
23.04(y2 " 2y # 1) " 1.96(x2 # 2x # 1) ! 24.0784 #
23.04 " 1.96
23.04(y " 1)2 " 1.96(x # 1)2 ! 45.1584
(y # 5)2
%
20
(y " 2)2
%
144
!1
center: ("1, 1)
y
a ! 1.4, b ! 4.8
vertices:
x
("1, 1 $ 1.4) or
O
(1, 2.4), (1, "0.4)
23.04y 2 # 46.08y # 1.96x 2 # 3.92x ! 24.0784
c2 ! a2 # b2
2
c ! 1.96 # 23.04
c2 ! 25
c !5
foci: ("1, 1 $5) or ("1, 6), ("1, "4)
1.4
7
% or $ %%
slopes of asymptotes: $%
4.8
24
25y2
"
(x " 5)2
%
576
(y " 1)2
%
1.96
y
(x # 4)2
%
25
"
center: (5, 0)
a ! 7, b ! 24
vertices: (5, 7), (5, "7)
c2 ! a2 # b2
c2 ! 49 # 576
c2 ! 625
c ! 25
foci: (5, 25), (5, "25)
slopes of asymptotes: $%27%
4
O
"8 "4 O
"4
576y2 ! 49x2 # 490x # 29,449
576y2 " 49x2 " 490x ! 29,449
576y2 " 49(x2 " 10x # 25) ! 29,449 " 1225
576y2 " 49(x " 5)2 ! 28,224
8
15.
!1
center: (0, 0)
a ! 4, b ! 7
vertices: (4, 0), ("4, 0)
c2 ! a2 # b2
c2 ! 16 # 49
c2 ! 65
c ! !6
"5
"
foci: (!6
"5
", 0), ("!6
"5
", 0)
slopes of asymptotes: $%74%
13.
4
!1
12. 49x2 " 16y2 ! 784
"
x
y
center: (0, 0)
a ! 3, b ! 2
vertices: (3, 0), ("3, 0)
c2 ! a2 # b2
c2 ! 9 # 4
c2 ! 13
c ! !1
"3
"
foci: (!1
"3
", 0), ("!1
"3
", 0)
slopes of asymptotes: $%23%
x2
%
16
14.
y
17.
16x2 " y2 # 96x # 8y # 112 ! 0
16x2 # 96x " y2 # 8y ! "112
16(x2 # 6x # 9) " (y2 " 8y # 16) ! "112 # 144 " 16
16(x # 3)2 " (y " 4)2 ! 16
(x # 3)2
%
1
"
(y " 4)2
%
16
center: ("3, 4)
a ! 1, b ! 4
vertices: ("3 $ 1, 4) or
("4, 4), ("2, 4)
c2 ! a2 # b2
c2 ! 1 # 16
c2 ! 17
c ! !1
"7
"
foci: ("3 $ !1
"7
", 4)
slopes of asymptotes: $%41%
456
!1
16x 2 # y 2 " 96x " 8y " 112 ! 0
y
12
8
4
"12 "8 "4 O
"4
4
8x
Algebra 2 Extra Practice
Page 893 Lesson 7-6
18. y2 " 4x2 " 2y " 16x # 1 ! 0
y2 " 2y # 1 " 4x2 " 16x ! 0
(y " 1)2 " 4(x2 " 4x # 4) ! "16
4(x " 2)2 " (y " 1)2 ! 16
(x " 2)2
%
4
"
(y " 1)2
%
16
1.
!1
(x " 2)2
%
4
center: (2, 1)
y
a ! 2, b ! 4
vertices: (2 $ 2, 1) or
(0, 1), (4, 1)
y 2 # 4x 2 # 2y # 16x " 1 ! 0
c2 ! a2 # b2
x
O
c2 ! 4 # 16
c2 ! 20
c ! 2!5
"
foci: (2 $ 2!5
", 1)
slopes of asymptotes: $%42% or $%21%
"
(x " 2)2
%
42
2.
!1
3.
$
%
225
25
675
% "12 y2 "5y # %% ! "60# %% "75
3 x2 #15x # %
4
4
4
$
15 2
%%
2
$ %
2
15 2
$x # %2%% " $y " %52%%
3 x#
%
" 12 y "
%%
11.25
$
5
,
center: "%12%
5 2
%%
2
%%
2.8125
c2 ! a2 # b2
c2 ! 11.25 # 2.8125
c2 ! 14.0625
c ! 3.75
5
foci: "%12%
$ 3.75, %52%
$
#
(y # 4)2
%
2
! 1; ellipse
y
x
O
x 2 " 4x " 2y 2 " 16y " 32 ! 0
(#2, #4)
x2 # 6x # y2 " 6y # 9 ! 0
# 6x # 9) # (y2 " 6y # 9) ! 9
(x # 3)2 # (y " 3)2 ! 9; circle
center: ("3, 3)
y
radius: !9
" or 3 units
x 2 " 6x " y 2 # 6 y " 9 ! 0
(x2
4.
4
5
%%
2
x
O
8
%
x
O
!1
y
$
y
(#3, 3)
%
5
vertices: "%12%
$ !1
"1
".2
"5
",
9x 2 # 36x " 36 ! 4y 2 " 24y " 72
135
%
!%
4
5
%%
2
a ! !1
"1
".2
"5
", b ! !2
".8
"1
"2
"5
"
! 1; hyperbola
x2 # 4x # 2y2 # 16y # 32 ! 0
# 4x # 4 # 2(y2 # 8y # 16) ! "32 # 4 # 32
(x # 2)2 # 2(y # 4)2 ! 4
center: ("2, "4)
"
a ! 2, b ! !2
length of major axis:
2(2) or 4
length of minor axis:
2!2
" or 2!2
"
3x2 " 12y2 # 45x # 60y ! "60
3x2 # 45x " 12y2 # 60y ! "60
%
x2
(x # 2)2
%
4
!4
"2
"
$
(y # 3)2
%
9
2
y
center: (2, 1)
"6
"8
" or 2!4
"2
",
a ! !1
12
b ! !4
"2
"
4
vertices: (2, 1 $ !1
"6
"8
")
c2 ! a2 # b2
8 16 x
"8 O
c2 ! 168 # 42
2
(y # 1) # 4(x # 2) 2 ! 168
c2 ! 210
c ! !2
"1
"0
"
foci: (2, 1 $ !2
"1
"0
")
"2
"
2!4
slopes of asymptotes: $ %
or $%21%
20.
"
center: (2, "3)
a ! 2, b ! 3
vertices: (2 $ 2, "3) or
(4, "3), (0, "3)
slopes of asymptotes: $%3%
19. (y " 1)2 " 4(x " 2)2 ! 168
(y " 1)2
%
168
9x2 " 36x # 36 ! 4y2 # 24y # 72
9(x2 " 4x # 4) " 4y2 " 24y ! 72
9(x " 2)2 " 4(y2 # 6y # 9) ! 72 " 36
9(x " 2)2 " 4(y # 3)2 ! 36
x
9y2 ! 25x2 # 400x # 1825
"
" 400x ! 1825
9y2 " 25(x2 # 16x # 64) ! 1825 " 1600
9y2
25x2
y2
%
25
"16 "12 "8 "4 O
4
"4
3x 2 # 12y 2 " 45x " 60y ! #60
"
(x # 8)2
%
9
! 1; hyperbola
center: ("8, 0)
a ! 5, b ! 3
vertices: ("8, 5), ("8, "5)
slopes of asymptotes: $%53%
%
!1
"1
".2
"5
"
slopes of asymptotes: $ %%
or $%21%
y
6
9y 2 ! 25x 2 " 400x " 1825
"12 "8 "4 O
"4
!2
".8
"1
"2
"5
"
2
x
"8
© Glencoe/McGraw-Hill
457
Algebra 2 Extra Practice
5.
6.
2y2 # 12y " x # 6 ! 0
2(y2 # 6y) # 6 ! x
2(y2 # 6y # 9) # 6 " 2(9) ! x
2(y # 3)2 " 12 ! x;
parabola
vertex: ("12, "3)
direction of opening:
right, since a & 0
y
10.
2y 2 " 12y # x " 6 ! 0
4
O
"8
x2
%
49
7.
#
y2
%
9
2
(y # 5)2 8
# (x " 1) 2 ! 4
4
4
"8 "4 O
"4
8
x2
%
1
x
12
y
9x 2 " 49y 2 ! 441
! 441; ellipse
4
(0, 0)
"8 "4 O
"4
"8
! 1; hyperbola
4x 2 # y 2 ! 4
13.
x
8
x2 # 4x # y2 " 8y ! 2
# 4x # 4 # y2 " 8y # 16 ! 2 # 4 # 16
(x # 2)2 # (y " 4)2 ! 22; circle
center: ("2, 4)
y
x 2 " 4x " y 2 # 8y ! 2
radius: !2
"2
" units
x2
8
(#2, 4)
"8
"12
3x 2 " y ! 12x # 17
center: (1, "5)
a ! 4, b ! 3
length of major axis:
2(4) or 8
length of minor axis:
2(3) or 6
#
(y # 5)2
%
9
14.
y
4
9x 2 # 18x " 16y 2 " 160y ! #265
4
8
x
12
"8
(x #
%
36
"
%
9
4
x
y
9x 2 " 9y 2 ! 9
1
(0, 0)
1
16. y " x2 ! x # 3
y ! x2 # x # 3
y ! x2 # x # %1% # 3 " %1%
y
$
4%
4
1 2
y ! $x # %%% # 2%3%; parabola
2
4
vertex: $"%1%, 2%3%%
2
4
x 2 " 10x " 5 ! 4y 2 " 16
4
"12 "8 "4 O
4x
"4
"8
© Glencoe/McGraw-Hill
"8 "4 O
"4
2x
"2
! 1; hyperbola
center: ("5, 0)
a ! 6, b ! 3
vertices: ("11, 0), (1, 0)
slopes of asymptotes: $%36% or $%12%
4
"2 "1 O
"1
x2 # 10x # 5 ! 4y2 # 16
# 10x " 4y2 ! 11
2
x # 10x # 25 " 4y2 ! 11 # 25
(x # 5)2 " 4y2 ! 36
x2
y2
y
12
(x " 3)2 ! 8(y " 2)
8
15. 9x2 # 9y2 ! 9
x2 # y2 ! 1; circle
center: (0, 0)
radius: 1 unit
(1, #5)
"12
5)2
(x # 3)2 ! 8(y # 2)
1
%%(x # 3)2 " 2 ! y; parabola
8
vertex : ("3, "2)
direction of opening:
upward, since a & 0
! 1; ellipse
"8 "4 O
"4
4x
"12 "8 "4 O
"4
9x2 " 18x # 16y2 # 160y ! "265
9(x2 " 2x # 1) # 16(y2 # 10y # 25) ! "265 # 9 # 400
9(x " 1)2 # 16(y # 5)2 ! 144
(x " 1)2
%
16
9.
x
O
"3x2
"4
8.
8x
4
y
center: (0, 0) a ! 1, b ! 2
vertices: (1, 0), ("1, 0)
slopes of asymptotes: $%21%
! 10x " 2y " 23
3x2 # y ! 12x " 17
# 12x " 17 ! y
"3(x2 " 4x # 4) " 17 # 3(4) ! y
"3(x " 2)2 " 5 ! y; parabola
vertex: (2, "5)
y
2
direction of opening:
O
"4
4
downward, since a ' 0
"
y2
%
4
8x
4
1
12. 4x2 " y2 ! 4
"4
x2 " y2
! 1; hyperbola
center: (0, 0)
a ! 7, b ! 3
length of major axis: 2(7) or 14
length of minor axis: 2(3) or 6
(5, 1)
4
(x # 1)2
%
4
11. 9x2 # 49y2 ! 441
x2 # y2 ! 10x # 2y # 23
2
x " 10x # y2 " 2y ! 23
2
(x " 10x # 25) # (y2 " 2y # 1) ! 23 # 25 # 1
(x " 5)2 # (y " 1)2 ! 49; circle
center: (5, 1)
y
8
radius: !4
"9
" or 7 units
O
"
y
12
center: ("1, 5)
a ! 4, b ! 2
vertices: ("1, 9), ("1, 1)
slopes of asymptotes: $%4% or $%2%
"4
4
" (x # 1)2 ! 4
(y " 5)2
%
16
x
"12 "8 "4
(y " 5)2
%
4
y
y # x2 ! x " 3
O
x
direction of opening: upward, since a & 0
458
Algebra 2 Extra Practice
17. 2x2 " 13y2 # 5 ! 0
13y2
%
5
"
2x2
%
5
y
! 1; hyperbola
center: (0, 0)
"2 "1 O
'(, b ! '(
vertices: $0, $'(%
a!
5
%
13
5
%
2
y2
# 11
%
3
2x
1
'(
2
%
13
18. 16(x " 3)2 # 81(y # 4)2 ! 1296
(x " 3)2
%
81
#
(y # 4)2
%
16
! 1; ellipse
center: (3, 4)
a ! 9, b ! 4
length of major axis:
2(9) or 18
length of minor axis:
2(4) or 8
y
4
16(x # 3)2 " 81(y " 4)2 ! 1296
"4 O
"4
4
8
12
x
(x " 1)2
%
5
2
"8
x2
%
4
"
y2
%
16
2
2
! 1; hyperbola
4x 2 # y 2 ! 16
20. x # 5y ! 16
x2
%
16
#
5y2
%
16
x 2 " 5y 2 ! 16
center: (0, 0)
'((
16
%%
5
(0, 0)
or
"
4!5
%
5
O
!
"6 $ !1
"2
"0
"
%%
14
!
"0
"
"3 $ !3
%%
7
!
x
#
y2
%
2
(x # 1)2
%
2
2
!1
!1
y!x#1
"3 " !3
"0
"
! %%
#1
7
4 # !3
"0
"
%%
7
!
"3 # !3
"0
" 4 # !3
"0
"
, %%
$ %%
%,
7
7
x2 # y2 ! 13
(#) x2 " y2 ! "5
2x2
! 8
x2
! 4
x ! $2
6.
y ! x2 " 4
y # 4! x2
x2
y2
% " % !1
5.
8!5
4!5
"
"
or %
$%
5 %
5
2
Page 894 Lesson 7-7
1.
4y # 4 ! x2
4(1) # 4 ! x2
8 ! x2
$!8
"!x
$2!2
"!x
($2!2
", 1)
x ! y2
4 ! y2
$2 ! y
25
y#4
%
25
4 " !3
"0
"
%%
7
"3 " !3
"0
" 4 " !3
"0
"
, %%
$ %%
%
7
7
x2 # y2 ! 13
($2)2 # y2 ! 13
y2 ! 9
y ! $3
($2, $3)
5
"
y2
%
5
2
!1
y # 4 " 5y ! 25
5y2 " y # 21 ! 0
y!
!
"("1) $ !"
(""
1"
)2"
""
4"
(5"
)("
2"
1")
%%%%
2(5)
1 $ !"
"4
"1
"9
"
%%
10
no real solutions
7. x2 # y ! 0
y ! "x2
x # y !"2
y ! "2 " x
(4, $2)
y ! "2 " x
! "2 " x
! "4
(2, "4)
© Glencoe/McGraw-Hill
!1
"6 $ !3
"6
""
""(7
4")(
""
"3
")"
%%%
2(7)
7
length of major axis: 2(4) or 8
length of minor axis:
4y ! x2 " 4
4y # 4 ! x2
x2 # y2 ! 9
(4y # 4) # y2 ! 9
y2 # 4y " 5 ! 0
(y # 5)(y " 1) ! 0
y # 5 ! 0 or y " 1 ! 0
y(
! "5
y!1
2.
(x # 3)2 # y2 ! 53
(x # 3)2 # x ! 53
2
x # 6x # 9 # x ! 53
x2 # 7x " 44 ! 0
(x # 11)(x " 4) ! 0
x # 11 ! 0 or x " 4 ! 0
x ! "11
(
x!4
#
y!x#1
"3 # !3
"0
"
! %%
#1
y
! 1; ellipse
a ! 4, b !
x!
x
O
1
2
(y # 2)
%
4
2
!1
2(x " 1) # 5(x # 1) ! 10
2(x2 " 2x # 1) # 5(x2 # 2x # 1) ! 10
2x2 " 4x # 2 # 5x2 # 10x # 5 " 10 ! 0
7x2 # 6x " 3 ! 0
y
center: (0, 0)
a ! 2, b ! 4
vertices: (2, 0), ("2, 0)
slopes of asymptotes:
$%4% or $%2%
2
(x " 1)2
%
5
4.
(3, #4)
19. 4x2 " y2 ! 16
"
(y # 2)2
%
4
4y2
"2
slopes of asymptotes: $
"
4(y2 # 11) " 3(y # 2) ! 12
# 44 " 3(y2 # 4y # 4) ! 12
4y2 # 44 " 3y2 " 12y " 12 " 12 ! 0
y2 " 12y # 20 ! 0
(y " 10)(y " 2) ! 0
y " 10 ! 0
or
y"2!0
y ! 10
y!2
2
2
2
2
x ! y # 11
x ! y # 11
x2 ! 102 # 11
x2 ! 22 # 11
2
x ! 111
x2 ! 15
x ! $!1
"1
"1
"
x ! $!1
"5
"
($!1
"1
"1
", 10),
($!1
"5
", 2)
"1
5
%
13
x2
%
3
3.
2
2x 2 # 13y 2 " 5 ! 0
1
459
"x2 ! "2 " x
"x"2!0
(x " 2)(x # 1) ! 0
x"2!0
or
x#1!0
x!2
x ! "1
x2
y ! "2 " x
! "2 " ("1)
! "1
("1, "1)
Algebra 2 Extra Practice
8.
Page 894 Lesson 8-1
x2 " 9y2 ! 36
x2 " 9(x)2 ! 36
"8x2 ! 36
6
x2 ! "%38%
no real solutions
1.
9. y2 " 16 ! 9x2
y2 ! 9x2 # 16
5x2 # y2 ! 30
y2 ! 9x2 # 16
2
2
5x # (9x # 16) ! 30
y2 ! 9($1)2 # 16
2
14x ! 14
y2 ! 9 # 16
x2 ! 1
y2 ! 25
x ! $1
y ! $5
($1, $5)
10.
y2
x2
%%
16
" %1% ) 1
center: (0, 0)
vertices: ($4, 0)
slopes of asymptotes: $%14%
y2
2
8
2.
x2 # y2 ) 49
center: (0, 0)
radius: 7 units
3.
x " y ! 49
4
"8 "4 O
"4
"8
11.
x2
%
25
"
y2
%
16
4
8x
4.
x2 y2
!1
#
16
1
)1
y*x"2
center: (0, 0)
vertices: ($5, 0)
slopes of asymptotes: $%45%
y
5.
x2 8 y2
!1
#
25 16
4
"8 "4 O
"4
4
"8
8x
y!x#2
12. y ! x # 3
8
4
7.
y
y!x"3
x2 # y2 ' 25
center: (0, 0)
radius: 5 units
8.
9.
"8 "4 O
4
8x
"4
"8
y 2 " x 2 ! 25
13. 4x2 # (y " 3)2 * 16
x2
%%
4
(y " 3)2
# %16% * 1
center: (0, 3)
length of major axis:
2(4) or 8
length of minor axis:
2(2) or 4
10.
x " 2y ! "1
"2y ! "x " 1
y ! %1%x # %1%
2
y
2
11.
12. "3[f(x)] ! "3
4x 2 " (y # 3) 2 ! 16
© Glencoe/McGraw-Hill
3
$%6x% " %29x% # 1%
3
2x
%"3
! "%2x% # %
3
x
O
p(x) ! 7x " 3
p(5) ! 7(5) " 3
! 35 " 3
! 32
p("1) ! 7("1) " 3
! "7 " 3
! "10
p(x) ! x2 # 5x " 4
p(5) ! "3 (5)2 # 5 (5) " 4
! "3(25) # 25 " 4
! "54
p("1) ! "3("1)2 # 5("1) " 4
! "3(1) " 5 " 4
! "12
p(x) ! 5x4 # 2x2 " 2x
p(5) ! 5(5)4 # 2(5)2 " 2(5)
! 5(625) # 2(25) " 10
! 3165
p("1) ! 5("1)4 # 2("1)2 " 2("1)
! 5(1) # 2(1) # 2
!9
p(x) ! "13x3 # 5x2 " 3x # 2
p(5) ! "13(5)3 # 5(5)2 " 3(5) # 2
! "13(125) # 5(25) " 15 # 2
! "1513
p("1) ! "13("1)3 # 5("1)2 " 3("1) # 2
! "13("1) # 5(1) # 3 # 2
! 23
6. p(x) ! %23%x2 # 5
p(x) ! x6 " 2
6
p(5) ! (5) " 2
p(5) ! %23% (5)2 # 5 (5)
! 15,625 " 2
! 15,623
! %23%(25) # 25
6
p("1) ! ("1) " 2
125
%
!%
3
!1"2
2
! "1
p("1) ! %3%("1)2 # 5("1)
g(x) ! 7x " 3
! %23%(1) " 5
g(a " 2) ! 7(a " 2) " 3
3
! 7a " 14 " 3
! "%13%
! 7a " 17
g(x) ! 3x # 5
g(a " 2) ! 3(a " 2) # 5
! 3a " 6 # 5
! 3a " 1
g(x) ! "(x # 2)2 # 8
g(a " 2) ! "[(a " 2) # 2]2 # 8
! "(a)2 # 8
! "a2 # 8
g(x) ! "2x3 # 5x
g(a " 2) ! "2(a " 2)3 # 5(a " 2)
! "2(a " 2)(a2 " 4a # 4) # 5a " 10
! "2(a3 " 6a2 # 12a " 8) # 5a " 10
! "2a3 # 12a2 " 24a # 16 # 5a " 10
! "2a3 # 12a2 " 19a # 6
"3[f(x)] ! "3(4x2 # 3x " 7)
! "12x2 " 9x # 21
3
x
2x
% " %% " 3
!%
2
3
x # 2y ! #1
460
Algebra 2 Extra Practice