Alg2 RBC Answers A - Mathematicsmathwithjp.weebly.com/uploads/2/0/8/8/20882022/hscc_alg2...opens up, the graph has two x-intercepts if the constant is negative and none if the constant

Answers

Copyright © Big Ideas Learning, LLC Algebra 2 All rights reserved. Answers

A21

153. ( ) 2 3g x x= − − 154. 47( ) 1g x x= +

155. ( ) 2 4g x x= + +

156. 12( ) 6 7g x x= − −

157. ( ) 3 5g x x= − − −

158. ( ) 1 2g x x= − + +

159. ( ) 3 1g x x= − −

160. 34( ) 5g x x= − +

Chapter 3 3.1 Start Thinking

Yes, there are patterns; Sample answer: A quadratic equation has one x-intercept when the vertex is on the x-axis. If the quadratic equation opens down, the graph has two x-intercepts if the constant is positive and none if the constant is negative. If the quadratic equation opens up, the graph has two x-intercepts if the constant is negative and none if the constant is positive; The vertex is a minimum if the 2x term is positive; The

vertex is a maximum if the 2x term is negative.

3.1 Warm Up

1. ( )4, 2− 2. ( )3, 4−

3. infinitely many solutions

4. no solution

5. 3 21

,11 11 −

or about ( )0.27, 1.91−

6. ( )1, 2− −

3.1 Cumulative Review Warm Up 1.

2.

3.

4.

3.1 Practice A 1. 5x = and 1x = 2. 3x =

3. 5x = and 5x = − 4. 2x = − and 6x =

5. 4x = and 4x = − 6. 3x = and 1

2x = −

−4 4 x

y

−2

2

y = −x2

y = x2 − 4

y = −x2 − 4

y = x2

Equation Number of x-intercepts Point(s)

2y x= 1 ( )0, 0

2y x= − 1 ( )0, 0

2 4y x= − 2 ( ) ( )2, 0 , 2, 0−

2 4y x= − − 0 N/A

x

y

−2

2−6

2

4

6

f(x) = (x + 4)2

x = −4

(−4, 0)

−2

−4

−6

x = 2

(2, −6)

x

y

531−2

g(x) = (x − 2)2 − 6

y = −5(x + 3)2 − 3

−2

−4

−6

−8

x = −3

(−3, −3)

x

y

2−2−4−6

f(x) = −x2 + 4

−2

2

x

y

3−3

(0, 4)

x = 0

Answers

Algebra 2 Copyright © Big Ideas Learning, LLC Answers All rights reserved. A22

7. 10t = and 10t = − 8. 8g = and 8g = −

9. 2y = and 6y = −

10. took the square root of each side before subtracting 16, and then incorrectly added the square roots of

the terms on the left side; ( )22 16 25;x − + =

( )22 9;x − = 2 3;x − = ± 2 3;x = ± 1x = −

and 5x =

11. 2x = and 2x = − 12. 2x = and 3x = −

13. 0m = and 4m = − 14. 9

15. 1 or 7

16. 2 10c = and 2 10;c = − Sample answer:

square root property; There is no linear term.

17. 0v = and 7;v = Sample answer: factoring and zero product property; The binomial is factorable.

18. no solution; left side always negative, right side positive

19. 8x = and 3;x = − Sample answer: factoring and

zero product property; The trinomial is factorable.

20. Sample answer: 2 10 24 0x x+ − =

3.1 Practice B

1. 1x = and 1x = − 2. 1x = and 1

3x = −

3. 7x = − and 2x = 4. 3

4x = and 3x = −

5. 2x = − and 6x = 6. 3x = − and 6x = −

7. 14k = and 8k = −

8. 1 3x = − + and 1 3x = − −

9. 3x = and 3x = −

10. Sample answer:

a. ( )22 4 20x − + =

b. ( )23 4 10x − + =

c. ( )22 10 4x − + =

11. 11x = and 11x = − 12. 9k = and 0k =

13. 5w = and 2w = − 14. 0y = and 3y =

15. 2

5x = and

3;

5x = Sample answer: Quadratic

Formula; The trinomial contains fractions.

16. 1.3n = and 1.3;n = − Sample answer: square

root property; There is no linear term.

17. 2 and 9− 18. 4 and 4−

19. 0 and 13 20. 4

3

21. $30 per rental; $720

22. ( ) 216 15; 0.968 sech t t t= − + ≈

3.1 Enrichment and Extension 1. 12 units 2. 16 in.

3. 3− or 2 4. 7 units by 15 units

5. 16 and 14 or 14− and 16−

6. 8 and 9 or 9− and 8−

7. 24− and 22− or 22 and 24

8. 16 and 9 9. 15 years old

10. 15 units by 17 units 11. 1 ft

12. 6 ft by 12 ft 13. 25 in.

14. 10 cm

3.1 Puzzle Time BUY A DECK OF CARDS

3.2 Start Thinking Most calculators will show an error screen instead of answering the keystrokes entered; There is no real number answer to the expression. Most calculators are not set up to consider the imaginary number set.

3.2 Warm Up 1. 10 32x + 2. 10 58y +

3. 12 18x + 4. 12 64x +

5. 7 10x + 6. 12 82x −

Answers


A23

3.2 Cumulative Review Warm Up

1. vertex: ( )4, 1 ,− − focus: 3

4, ,4

−

directrix:

11,

4y = − axis of symmetry: 4x = −

2. vertex: ( )4, 0 ,− focus: 15

4, ,4

−

directrix:

15,

4y = − axis of symmetry: 4x = −

3. vertex: ( )3, 0 , focus: ( )3, 2 ,− directrix: 2,y =

axis of symmetry: 3x =

4. vertex: ( )4, 4 , focus: ( )4, 5 , directrix: 3,y =

axis of symmetry: 4x =

3.2 Practice A 1. 5i 2. 9i

3. 4 2i 4. 3x = and 3y =

5. 2x = − and 5y = 6. 13x = and 4y =

7. 6x = and 10y = − 8. 8 9i+

9. 13 i− 10. 2 2i+

11. 3 i− −

12. a. 0 11i+

b. ( )0 3 3 1 i+ −

13. 10 20i− − 14. 9 24i+

15. 7 i− 16. 48 46i+

17.

18. 3i and 3i− 19. 7i and 7i−

20. 6x i= and 6x i= −

21. 2 5x i= and 2 5x i= −

3.2 Practice B

1. 15i 2. 4 10i

3. 12 6i 4. 7x = and 4y = −

5. 24x = and 2y = 6. 11x = and 10y = −

7. 1x = and 10

3y = 8. 6 13i− +

9. 8 6i+ 10. 3 15i− +

11. 5 i+

12. a. 2 3i− −

b. 4 4i− +

c. 5 2i−

13. 6 43i+ 14. 34 0i+

15. 149 0i+ 16. 20 48i−

17.

18. 4 3i and 4 3i−

19. 2 13i and 2 13i−

20. 2 11x i= and 2 11x i= −

21. 3 5x i= and 3 5x i= −

3.2 Enrichment and Extension

1. 3 6

5 5i− 2.

1 1

2 2i+

3. 1 0i− + 4. 1 4

3 3i− −

5. 2 14

25 25i− − 6. 132 24

25 25i−

( )[ 14 5 3 ] 4i i+ − − Definition of complex addition

( )19 3 4i i− − Simplify.

( )19 3 4i i+ − − Definition of complex addition

19 7i− Write in standard form.

248 18 16 6i i i− − + Multiply using FOIL.

248 34 6i i− + Simplify and use

2 1.i = −

( )48 34 6 1i− + − Simplify.

42 34i− Write in standard form.

Answers


7−18.

19. Complex numbers and their conjugates are the reflection of one another in the real axis.

20. 0,a = so a bi+ is a pure imaginary number.

3.2 Puzzle Time YOU’D KNOW THE DIFFERENCE IF YOU EVER LET A PTERODACTYL SIT ON YOUR SHOULDER

3.3 Start Thinking 2 8 16;x x+ + To find the middle term, multiply the

terms inside the parentheses and then multiply the result by 2. To find the last term, square the second term

inside the parentheses; ( )22 6 9 3 ,a a a+ + = +

( )22 14 49 7 ;b b b+ + = + You could take the

coefficient of the middle term, divide it by 2, and then square the result.

3.3 Warm Up

1. ( )( )5 5z y z y+ − 2. ( )( )5 1 5 1x x+ −

3. ( )27 2x y+ 4.

1 11 1

x x + −

5. ( )( )2 2 1 2 1y y+ − 6. ( )22 1r s −

3.3 Cumulative Review Warm Up 1. absolute value, domain: all real numbers, range:

0y ≥

2. linear, domain: all real numbers, range: all real numbers

3. quadratic, domain: all real numbers, range: 1y ≥

4. absolute value, domain: all real numbers, range: 1y ≥ −

5. linear, domain: all real numbers, range: all real numbers

6. quadratic, domain: all real numbers, range: 5y ≤ −

3.3 Practice A 1. 5x = and 1x = − 2. 13y = and 1y = −

3. 10 2 10n = + and 10 2 10n = −

4. 7 2p = − + and 7 2p = − −

5. ( )216; 4c x= + 6. ( )2

49; 7c x= +

7. ( )281; 9c y= −

8. ( )2169; 13c y= +

9. 4 11x = − + and 4 11x = −

10. 5 29h = + and 5 29h = −

11. 6 26t = + and 6 26t = −

12. 7 58s = − + and 7 58s = − −

13. 3 11y = − + and 3 11y = − −

14. 5 19g = − + and 5 19g = − −

15. square roots; Both sides are perfect squares; 8x =and 2x = −

16. factoring; factorable; 4x = − and 1x = −

17. Sample answer: factoring and square roots; factorable, both sides are perfect squares; 3x =

18. completing the square; even middle term;

5 33x = + and 5 33x = −

19. 4 20. 2 2 6− +

21. ( ) ( ) ( )25 7; 5, 7f x x= + + −

22. ( ) ( ) ( )23 11; 3, 11g x x= − − −

3.3 Practice B 1. 20w = and 2w =

2. 8 2 2k i= + and 8 2 2k i= −

3. 15 2 6t i= + and 15 2 6t i= −

2

4

−2

−4

2 4−2−4−6 real

imaginary6

Answers


A25

4. 1 2 3

3p

− += and

1 2 3

3p

− −=

5. ( )264; 8c x= + 6.

249 7

;4 2

c x = +

7. 2

9 3;

4 2c y

= −

8. ( )2100; 10c y= +

9. 3 10q = − + and 3 10q = − −

10. 1 13

2 2h = +

and

1 13

2 2h = −

11. 4 11x = − + and 4 11x = − −

12. 6y = and 2y =

13. 2 6t = + and 2 6t = −

14. 5 31

2 2s = − + and

5 31

2 2s = − −

15. square roots; Both sides are perfect squares; 16x = − and 2x = −

16. completing the square; not factorable;

211

3x = − +

and

211

3x = − −

17. Sample answer: factoring; factorable; 12x = and 12x = −

18. factoring; factorable; 3x = and 3x = −

19. ( ) ( ) ( )29 19; 9, 19f x x= + + −

20. ( ) ( ) ( )21 27; 1, 27g x x= − − −

21. ( ) ( ) ( )211 25; 11, 25h x x= + − − −

22. ( )2

1 7 1 7; ,

2 4 2 4f x x

= − +

23. a. 18 ft

b. 11

14

t = + sec or 1.8t ≈ sec


1. ( ) ( ) ( )24 0 0; 0, 0 ; 0f x x x= − + =

The graph is a vertical stretch by a factor of 4 of the graph of the parent quadratic function.

2. ( ) ( ) ( )20 3; 0, 3 ; 3 1.73f x x x= − − + = − ≈ −

and 3 1.73x = ≈

The graph is a reflection in the x-axis followed by a vertical translation 3 units up of the graph of the parent quadratic function.

3. ( )2

5 25 5 25; , ; 0

2 4 2 4f x x x

= − − − =

and

5x =

The graph is a horizontal translation 5

2 units right

followed by a vertical translation 25

4 units down of

the graph of the parent quadratic function.

4

6

−2

2 x4−2−4

y

f(x) = 4x2

2

4

6

−2

x4−4

y

f(x) = −x2 + 3

−2

−4

−6

2 x4 6−2

y

f(x) = x2 − 5x

Answers


4. ( ) ( ) ( )24 5; 4, 5 ;f x x= + − − −

4 5 6.24x = − − ≈ − and

4 5 1.76x = − + ≈ −

The graph is a horizontal translation 4 units left followed by a vertical translation 5 units down of the graph of the parent quadratic function.

5. ( ) ( ) ( )23 1 6; 1, 6 ;f x x= − − − −

no x-intercepts

The graph is a reflection in the x-axis followed by a vertical stretch by a factor of 3, and a horizontal translation 1 unit right and vertical translation 6 units down of the graph of the parent quadratic function.

6. ( ) ( ) ( )22 3 5; 3, 5 ;f x x= + − − −

103 4.58

2x = − − ≈ − and

103 1.42

2x = − + ≈ −

The graph is a vertical stretch by a factor of 2 followed by horizontal translation 3 units left and vertical translation 5 units down of the graph of the parent quadratic function.

3.3 Puzzle Time ONLINE SKATER

3.4 Start Thinking Sample answer: completing the square: Use when

1a = and b is even. Also, use when there is no c term; factoring: Use when the function is easily factorable; graphing: Use when the equation includes decimals or when approximated answers are accepted; using square roots: Use when the algebraic expression is a perfect square; graphing, using square roots, factoring, completing the square

3.4 Warm Up

1. 3

2 2. 1− 3. 4−

4. 4 5. 16 6. 6

5−


1. ( ) 6 3g x x= − 2. ( ) 15

3g x x= − +

3.4 Practice A

1. 9 65

2x

− ±= 2. 1x = − and 2x =

3. 3x = − 4. 1

4x =

and 1x = −

5. 5 23

6 6x i= ± 6. 12x =

7. 7 23

4 4x i

−= ± 8. 1 5 2

3 6x i= ±

9. 12; two real solutions 10. 0; one real solution

11. 207;− two imaginary solutions

12. 16; two real solutions 13. B

14. Sample answer: 21; 16; 8 16 0a c x x= = + + =

15. Sample answer: 22; 10; 2 5 10 0a c x x= = − + =

16. 24 9 10 0x x− + = 17. 23 11 2 0x x− + − =

18. 2;

3x = square root; perfect square

−2

−4

x−4

y

2

4

f(x) = x2 + 8x + 11

2 x4−2−4

y

−2

−4

−6

−8

f(x) = −3x2 + 6x − 9

−2

−4

x−2−6

y

2

4

2

f(x) = 2x2 + 12x + 13

Answers


A27

19. 3x = and 1

;4

x = Quadratic Formula; difficult to

factor

20. 6 3 3;x = ± complete the square; even middle

term and leading coefficient of 1

21. 2x = − and 6;x = factoring; easy to factor

22. 2 4 0

1 4 0

1

4

b ac

c

c

− >− >

<

3.4 Practice B

1. 4x = − and 1x = 2. 1x = −

3. 5 55

2 2x i= − ± 4.

3 89

8x

±=

5. 6 51x = − ± 6. 66

13

x i= ±

7. 5 21v = ± 8. 4 2

3 3t i= ±


10. 0; one real solution 11. 132; two real solutions


13. C

14. Sample answer: 21; 7; 3 7 0a c x x= = − − − =

15. Sample answer: 24; 12; 4 10 12 0a c x x= = + + =

16. 27 10 6 0x x− + = 17. 24 3 1 0x x+ − =

18. 1;x = square root; perfect square after factoring

out 7

19. 10 6 3;x = − ± complete the square; even

middle term and leading coefficient of 1

20. 1 7

;2 2

x i= − ± Quadratic Formula; odd middle

term

21. 2x = and 4;x = factoring; easy to factor

22. 2 4 0

1 4 0

1

4

b ac

c

c

− <− <

>


1. 1x = and 1

;8

x = − yes

2. 5

2x = −

and

4;

3x = yes

3. 1x = − and 7;x = yes

4. 2

3x = −

and

4;

5x = yes

5. 2.25x = − and 14;x = yes

6. 2x = and 20

;7

x = − yes

7. one real solution; 0x =

8. two real solutions; 3x = − and 3x =

9. two real solutions; 0x = and 5x =

4

6

−2

2 x4−2−4

y

f(x) = 4x2

2

4

−2

x4−4

y

f(x) = −x2 + 3

−2

−4

−6

2 x4 6−2

y

f(x) = x2 − 5x

Answers


10. The average of the x-intercepts is the x-value of the vertex.

3.4 Puzzle Time SOFA SO GOOD

3.5 Start Thinking

Sample answer:

system with one linear equation and one quadratic equation, two points of intersection:

system with two quadratic equations, one point of intersection:

system with two quadratic equations, two points of intersection:

3.5 Warm Up

1. ( )3.4, 1.4− 2. ( )0, 0 3. ( )2, 1−



1.

2.

3.

4.

3.5 Practice A

1. ( ) ( )6, 0 and 4, 2− − 2. ( )2, 3− −

3. ( ) ( )0, 3 and 1, 2 4. ( ) ( )1, 1 and 4, 5−

5. ( )1, 2 6. no solution

7. ( ) ( )1, 3 and 4, 0− 8. ( ) ( )0, 5 and 5, 0

9. ( )1, 0 10. ( ) 11,7 and , 7

4 −

11. ( )3, 8−

2

4

−4

x42−4 −2

y

y = x2 − 2

y = x

2

4

−4

−2

x42−4 −2

y

y = x2

y = −x2

4

8

−8

−4

x42−4 −2

y

y = x2 − 10

y = −x2 + 10

2

4

6

x4 6 82

y

f(x) = (x − 5)2

4

12

16

x42−4 −2

y

g(x) = (x + 1)2 + 7

y = −6(x − 4)2 + 2

−2

−4

2

x

y

2 4 6

f(x) = −2(x − 1)2 − 5−2

−4

−6

x

y

2 4−2

Answers


A29

12. ( ) ( )0.25, 7.5 and 1, 10− − −

13. no solution 14. ( ) ( )3, 3 and 1, 3

15. The horizontal line cuts through the circle, intersecting in two places.

3.5 Practice B

1. no solution 2. ( ) ( )1, 3 and 2, 6− −

3. ( ) ( )0, 9 and 3, 0− − 4. ( )1, 2

5. ( ) ( )0.27, 0 and 3.7, 0 6. ( ) ( )0, 6 and 2, 2−

7. ( ) ( )1, 2 and 1, 2− − − 8. ( )1, 0

9. no solution 10. ( ) ( )3, 2 and 2, 3− −

11. no solution 12. ( ) ( )8, 32 and 2, 2−

13. ( ) ( )4, 24 and 2, 12− − 14. ( ) 73, 8 and , 8

3 − −

15. The horizontal line is tangent to the circle either at the top or the bottom.


1. parabola; ( )291 3

4y x= − −

2. circle; ( ) ( )2 21 1 8x y− + − =

3. hyperbola; ( ) ( )2 2

2 31

5 20

x y+ +− =

4. parabola; ( )23 4y x= + −

5. circle; ( ) ( )2 21 3 25x y+ + + =

6. hyperbola: ( ) ( )2 2

1 21

9 4

x y+ −− =

3.5 Puzzle Time

SPUDNIK

3.6 Start Thinking

Sample answer:

Graph the parabola with 2 .y x bx c= + + Make the

parabola dashed for inequalities with or< > and solid

for inequalities with or≤ ≥ .

Test a point ( ),x y inside the parabola to determine

whether the point is a solution to the inequality.

Shade the region inside the parabola if the point is a solution. Shade the region outside the parabola if the point is not a solution.

3.6 Warm Up

1. 2.

3. 4.


1. 8

1

6

x

y

z

== −=

2. 2

4

7

x

y

z

= −= −=

3.6 Practice A

1. 2.

2

x

4−2−4

y

−2

−4

−8

y > x − 5

−2

−4

2

x

y

2 4−2−4y ≥ −3

2

4

x

y

2 4−2−4

y > 2x − 53

4

2

6

−2

2 x4−2−4

y

y > x2

2 x4−2−4

y

−6

1

y ≤ −3x2

8

4

2 x4−2

y

y > −2x + 10

Answers


3. 4.

5. ( )y f x≥ 6. ( )y f x≤

7.

8.

9. 4 4or

3 3x x< − > 10. 1 or 7x x≤ ≥

11. 7 3x− ≤ ≤ − 12. 91

2x< <

13. all real numbers 14. 5.54 0.54x− ≤ ≤

15. 5 1x− ≤ ≤ −

16. 3.73 or 0.27x x< − > −

17. a. 2125 2500w w− ≥

b. 25 100w≤ ≤

3.6 Practice B

1.

2.

3.

4.

5. wrong side was shaded

6.

7.

x4−4

y

−6

−2

2

y ≥ x2 − 5

−2

−4

4

x

y

2 4−2−4

y < x2 − 3x

4

6

8

2

x

y

2 4−2−4

y ≤ x2 + 3

−4

4

2

x

y

2 4−2−4

y ≤ −2x2

y > x2 − 3

4

x

y

2 4−2−4

y < 2x2 − 4

y < 4x2

−2

−4

4

x

y

2 4−4

y < −(x + 1)2 + 2

4

2

x

y

2 5−2

y ≥ −x2 + 4x

−2

−4

4

x

y

2 4−4 −2

y < −x2 + 2

−4

−2

x

y

4−4

y ≥ 2x2 − 3x + 1

y ≤ −x2 + 3

8

16

24

y

x2 4 6

y > x2 − x + 4

y < x2 + 2x − 4

−2

4

2

x

y

2 4−2−4

y > x2 + 2x − 3

Answers


A31

8. 1or 6

2x x> < − 9. 1

22

x≤ ≤

10. 3 13 or 3 13x x≤ − − ≥ − +

11. 3 9x− < < 12. 2.64 or 1.14x x< − >

13. 1.66 0.91x− ≤ ≤ 14. 3.24 1.24x− ≤ ≤

15. 4.37 or 1.37x x< − >

16. a. 25 ft; ( ) 25h t = when 0.t =

b. 216 28 25 0t t− − + >

c. 0 0.65t< <


a. ( ) 22 370R x x x= − +

b. $17,112

c. 92 or 93

d. ( ) 30 312C x x= +

e. ( ) 22 340 312 0P x x x= − + − >

f. between 1 and 169, including 1 and 169

g. $14,138; 85 handbags

3.6 Puzzle Time

BAGELS

Cumulative Review

1. 5 2 2. 3 5 3. 4 6

4. 8 3 5. 10 3 6. 3 6−

7. 5 7− 8. 6 2− 9. 5

6

10. 6

7 11.

3

2 12.

7

3

13. 1

4 14. 2

5− 15.

7

9−

16. 5

8− 17. 3 18. 0

19. 2 20. 3 21. 11

22. 10 23. 67 24. 1

25. 46 5x− + 26. 28 22x +

27. 27 12 8x x+ − 28. 2 20 15x x+ −

29. 33 24x − 30. 2 25 35x x− + −

31. 3 227 7 41 9x x x− + +

32. 5 4 24 16 7 6x x x x− + − − −

33. 3 28 10 22 19x x x+ + +

34. 4 3 210 35 19 8 20x x x x− + − + −

35. a. 20.4 min b. 21 min c. 1.1 min

36. 24 40 44x x− + 37. 210 5 15x x− + +

38. 2 6 8x x+ + 39. 2 3 2x x− +

40. 220 5 90x x− + +

41. 3 26 21 22 77x x x− − +

42. 3 212 142 60 14x x x− + +

43. 4 3 230 40 21 8 3x x x x− + − +

44. 3 284 164 79 9x x x− − − −

45. 4 3 24 30 116 99x x x x− − + −

46. 5 4 3 22 12 5 58 129 11x x x x x− + − + − −

47. 4 3 26 65 53 156 60x x x x+ + − +

Number of handbags purchased

Price per handbag (dollars)

Revenue per order

(dollars)

1 368 368

2 366 732

3 364 1092

4 362 1448

5 360 1800

6 358 2148

x 370 2x− ( )370 2x x−

Answers


48. 24 28 12x x+ + 49. 210 25 50x x− − +

50. 2 16 48x x+ + 51. 28 160 792x x− + −

52. 23 6 9x x+ − 53. 216 12 28x x− −

54. 296 444 462x x− − + 55. 22 20 10x x+ −

56. 27 23 17x x+ − 57. 254 9 31x x+ +

58. 26 47 28x x− − − 59. 24 21 87x x+ −

60. a. 95 items

b. 22 items

61. brother 7 min, sister 12 min= =

62. a. width 14 ft, length 19 ft= =

b. $1056

c. 266 ft2

63. 4, 7x x= − = 64. 2, 3x x= =

65. 7, 9x x= − = 66. 51,

2x x= − =

67. 93,

4x x= − = − 68. 2

3,5

x x= − =

69. 2 7,

3 5x x= − = 70. 5 7

,4 2

x x= =

71. 1 1,

4 6x x= − = 72. 3 1

,7 12

x x= − =

73. 4 1,

7 4x x= − = 74. 1 9

,5 8

x x= − =

75. 512,

6x x= − = 76. 5 10

,2 11

x x= − =

77. 4 6,

3 11x x= − = 78. 9y x= +

79. 15

2y x= + 80. 3 17y x= −

81. 2 4y x= − 82. 11 23y x= −

83. 3 5

4 4y x= − + 84. 6 3y x= +

85. 5 9y x= + 86. 14 21y x= − +

87. 6 24y x= − 88. 2 28y x= − +

89. 45 20y x= − 90. 108−

91. 524− 92. 448 93. 368

94. 57 95. 53 96. 20−

97. 28− 98. 279− 99. 116−

100. 73 101. 4−

102. a. ( ) ( )4 18b b+ + =

b. 11 baskets

c. 7 baskets

103. a. 55 mi/h

b. 2.75 h

104. 8, 10x x= − = 105. 34, 22x x= − =

106. 0, 4x x= = 107. 14, 6x x= − =

108. 13, 3x x= − = 109. 9, 25x x= − =

110. 11 13,

3 3x x= = 111. 18, 12x x= − =

112. no solution 113. ( )7, 3−

114. ( )4, 2− − 115. no solution

116. ( )6, 6−


118. ( )5, 7− 119. ( )3, 4, 6−

120. ( )9, 8, 2− 121. ( )6, 2, 1− −


123. ( )2, 1, 4− − 124. no solution

125. 6 15i+ 126. 12 10i− +

127. 5 5i− − 128. 7 18i−

129. 9 7i+ 130. 12 8i− −

131. 2 2i+ 132. 2i

133. 26 3i− 134. 11 22i+

Answers


A33

135. 16 72i+ 136. 60 24i− −

137. 39 4i− − 138. 79 16i+

139. 47 i− 140. 27 36i−

141. 23 264i− + 142. 80 18i+

143. a. 23 lb

b. $0.45

c. about $0.91

Chapter 4 4.1 Start Thinking

The graph of ( ) 3f x x= is a curvy line that is moving

upward from left to right as x increases. The graph of

( ) 4g x x= is similar to a parabola that opens up with

its vertex at the origin. Both graphs have positive y-values when x is positive. When x is negative, the y-values of ( )f x are negative, and the y-values of

( )g x are positive; The exponent is even; yes; ( )0, 0

and ( )1, 1

4.1 Warm Up

1. 20− 2. 39 3. 10

4. 40 5. 45.8− 6. 33.96


1. down 2. up 3. down 4. up

4.1 Practice A

1. polynomial function;

( ) 3 25 4 3 7,f x x x x= + − − degree is 3, cubic,

leading coefficient is 5

2. not a polynomial function


( ) 4 3 214 2 10,

3g x x x x x= − − + + degree is 4,

quartic, leading coefficient is 1

4. polynomial function; ( ) 28 3 2,f x x x= − +

degree is 2, quadratic, leading coefficient is 8

5. 2− 6. 6848 7. 15,651

8. ( )g x → +∞ as x → +∞ and ( )g x → +∞ as .x → −∞

9. ( )h x → −∞ as x → +∞ and ( )h x → +∞ as .x → −∞

10. 11.

12. 13.

14. f is increasing when 3.x > f is decreasing when 3.x < f is positive when 2x < and 4.x > f is

negative when 2 4.x< <

15. f is increasing when 1.2x < − and 1.2.x > f is

decreasing when 1.2 1.2.x− < < f is positive

when 2 0x− < < and 2.x > f is negative when

2x < − and 0 2.x< <

16. The degree is even and the leading coefficient is negative.

4.1 Practice B


2. polynomial function; ( ) 211 12 7,f x x x= + −

degree is 2, quadratic, leading coefficient is 11


( ) 4 3 21 52 14 2 ,

3 3g x x x x x= − − + − degree

is 4, quartic, leading coefficient is 2


5. 1841 6. 479

− 7. 58

−

5

−5

−5

5

g(x) = x4

f(x) = x3

x

y4

2

−4

42−2−4

q(x) = x4 − 2

x

y

2

2

h(x) = x3 − 2x + 3

x

y

2

2−2

k(x) = 2x2 + 3 − x3

x

y

4

2

2−2

f(x) = x5 − 2x3 + 1

Documents

Alg2 RBC Answers A - Mathematicsmathwithjp.weebly.com/uploads/2/0/8/8/20882022/hscc_alg2...opens up, the graph has two x-intercepts if the constant is negative and none if the constant