Chapter 8 Review Answers

1A. Points include: (-2, .014), (-1, .05), (0, .2), (1, .76), (2, 2.9)
1B. Points include: (-2, 48), (-1, 12), (0, 3), (1, .75), (2, .19)

2A. y = .0015 (10)^x
2B. y = 1 (1/3)^x

3A. y = 12500(.91)^x, and y = $7800 after 5 years
3B. y = 50 (1.03)^x and y = $57.96 after 5 years

4A. translation shifts down 5 from the parent
4B. translation shifts 2 to the right and up 3 from the parent

5A. log (base 6) 36 = 2
5B. log (base 3) 27 = 3

6A. log (base 2) .125 = -3
6B. log .001 = -3

7A. 6
7B. 0

8A. -2
8B. -3

9A. log 192
9B. log (base 3) (7x^4)

10A. log (base 2) (5/3)
10B. log (y^3/z)

11A. 2log (base 2) x + 3 log (base 2) y
11B. log 6 + 4 log s - log t

12A. log (base 3) 2 - log (base 3) x
12B. 5 log (base 6) x + 10 log (base 6) y - 2 log (base 6) z

13A. 2.3774
13B. 3.0589

14A. .6599
14B. .6658

15A. 10/3
15B. 8

16A. 5.1962
16B. 500

17A. 18.19 hours
17B. 28.21 years

18A. .8283
18B. 3.7726

19A. 4.307
19B. 1.82 x 10^-4

20A. $301.11
20B. $1169.82

Period 2 Chapter 6 Retake Review

degree 2: quadratic, degree 3: cubic
degree 4: quartic, degree 5: quintic

1 term: linear, 2 terms: binomial, 3 terms: trinomial

1A. x^5 - x^3 + x, quintic, trinomial

1B. 4x^3 + 2x^2 + 2x, cubic, trinomial

2A. y = (2.04x10^-4)x^3 + .26 x^2 - 3.62 x + 29.3

2B. $414.93

Imaginary zeros/roots come in pairs called CONJUGATES.

3A. x^3 - 4 x^2 - 11 x + 30

3B. x^3 + 6 x^2 + 9 x + 54

To find the zeros of a function, FIRST MAKE IT EUQAL TO ZERO, then SOLVE FOR x.

Multiplicity: THE NUMBER OF TIMES A FACTOR OR ZERO APPEARS

4A. x = -1 (mult. of 2), x = 3/5 (mult. of 1)

4B. x = 0 (mult. of 1), x = 2 (mult. of 3), x = -1/2 (mult. of 1)

FACTORING CHECK LIST:
1. Check for a GREATEST COMMON FACTOR. Continue factoring.

2. Check for a DIFFERENCE OF TWO SQUARES. Continue factoring.
Pattern: a^2 - b^2 = (a + b)(a - b)

3. Check for a SUM OR DIFFERENCE OF TWO CUBES.
Pattern: a^3 - b^3 = (a - b)(a^2 + ab + b^2)
Pattern: a^3 + b^3 = (a + b)(a^2 - ab + b^2)

4. Check for a SUBSTITUTION TO MAKE A NICE QUADRATIC.

5A. 3x^2 (x - 2)(x + 1) =0
x = 0, x = 2, x = -1

5B. 4x (x + 5)(x - 2) = 0
x = 0, x = -5, x = 2

6A. 2 (x + 3)(x^2 - 3x + 9) = 0
x = -3, x = (-3 +/- 3i sqrt3) / 2

6B. (2x - 5)(4x^2 + 10x + 25) = 0
x = 5/2, x = (-5 +/-5i sqrt5) / 4

7A. (x + 10)(x - 10) = 0
x = -10, x = 10

7B. 3 (x + 4)(x - 4) = 0
x = -4, x = 4

8A. 2(x^2 - 14)(x^2 + 1) = 0
x = +/- sqrt14, x = +/- i

8B. (x^2 + 3)(x^2 + 5) = 0
x = +/- i sqrt 3, x = +/- i sqrt5

9A. (x + 1)(x - 3)(x - 4)

9B. (x - 3)(x - 3)(x + 2)

10A. complex roots: 3, possible real roots: 1, 3

10B. complex roots: 4, possible real roots: 0, 2, 4

11A. This is really tough! Don't even try p/q--it won't work because the last term is 36x. Instead, look for a GCF, then go through the rest of the factoring check list.
x = 0, x = +/- 3, x = +/- 2i

11B. This is also tough! Look for a GCF, then go through the rest of the factoring check list.
x = +/- sqrt14, x = +/- i

12A. x = -4, x = +/-i sqrt7

12B. x = -2, x = 1 +/- sqrt7

Chapter 6 Review

I have to warn you that the formatting is not as nice as if you were looking at a regular Word document--the post editor won't let me cut-and-paste from a Word document, and I couldn't find a way to type nice exponents.

Here's the best I could do:
"x squared" looks like "x^2"
"plus or minus" looks like +/-
"square root" looks like "sqrt"

Leave your name and a comment if you have a question, and I will reply by leaving a comment.

1A. x^5 - x^3 + x --> quintic trinomial

1B. 2x^2 + 2x --> quadratic binomial

2A. y = -.04x^3 + .65x^2 - 2.94x + 24.84 --> y=7.33 when x = 12

3A. y = x^3 - x^2 -25x + 25

3B. y = x^3 + 6x^2 + 12x + 8

4A. 3x^2 (x - 2)(x + 1)

4B. 4x (x + 5)(x - 2)

5A. x = -1 --> multiplicity 2 AND x = 3

5B. x = 0 & x = 2 -->multiplicity 3 AND x = -5

6A. x^3 + 3x^2 + 3x +4, R1

6B. 3x^2 - 7x + 7, R-8

7A. remainder = 0 --> yes, x - 3 is a factor

7B. remainder = 1 -->no, x-3 is not a factor

8A. P(-2) = 77

8B. P(3) = 153

9A. (x + 1)(x - 1)(x - 3)

9B. (x - 3)(x - 3)(x + 2)

10A. for periods 5, 7:
max = 3.08 (at x = -.15) AND min = -3.08 (at x = 2.15)

10A. for period 6:
The polynomial from 9A doesn't really have a relative max/min.
Instead, try x^3 - 3x^2 - x + 3 and check the answers for periods 3, 5

10B. for periods 5, 7:
max = 0 (at x =0) AND min = -1.26 (at x = .82) AND min = -45.1 (at x = -3.07)

10B. for period 6:
max = 18.5 (at x = -.33) AND min = 0 (at x =3)
Or try x^4 + 3x^3 - 5x^2 and check the answers for periods 3, 5

11A. factored: 2(x + 3)(x^2 - 3x + 9) = 0
solutions: x = -3 AND x = (3 +/- 3i sqrt3)/2

11B. factored: (2x - 5)(4x^2 + 10x + 25) = 0
solutions: x = 5/2 AND x = (-5 +/- 5i sqrt3)/4

12A. factored: (x + 10)(x - 10) = 0
solutions: x = -10 AND x = 10

12B. factored: 3(x + 4)(x - 4) = 0
solutions: x = -4 AND x = 4

13A. x = +/- sqrt14 AND x = +/- i

13B. x = +/- i sqrt3 AND x = i sqrt5

14A. 3 - 2i and 1 - sqrt2

14B. 2 + sqrt3

15A. y = x^3 - 2x^2 + x - 2

15B. y = x^4 -10x^3 + 39x^2 - 70x + 50

16A. complex: 3, real: 1 or 3
possible rational roots: +/- 1, +/-3, +/-5, +/-15

16B. complex: 4, real: 0, 2, or 4
possible rational roots: +/-1, +/-2, +/-4, +/-1/3, +/-2/3, +/-4/3

17A. x = 0, x = +/-3, x = +/- 2i

17B. x = +/-2 sqrt2, x = +/- i sqrt6

18A. x = 4, x = +/- i sqrt7

18B. x = -2, x = 1 +/- sqrt7

I told you I'd do it...

Check back here over the weekend for answers to the Chapter 6 Review!