Algebra 2 Distance Learning Packet

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Virtual Office Hours: 9:00 a.m.- 11:00 a.m. & 1:00 p.m.- 3:00 p.m. Conference Call Dial-in Number: ______Dial-in Access Code: ______

Online Meeting URL: ______Online Meeting ID: ______

April 13 April 14 April 15 April 16 April 17 Standard: A2.AAPR.3 Standard: A2.AAPR.3 Standard: A2.AAPR.3 Standard: A2.AAPR.3 Standard: A2.AAPR.3

Learning Tasks: Learning Tasks: Learning Tasks: Learning Tasks: Learning Tasks: Complete 4-4 Study Guide and 4-4 Complete 4-5 Study Guide and Graph your assigned polynomial Determine the characteristics of Write a paragraph describing the Word Problem Practice Intervention & Skills Practice function. your assigned polynomial characteristics of your assigned function. polynomial function.

Extension Activities Extension Activities Extension Activities Extension Activities Extension Activities Khan Academy Polynomial Graphs Khan Academy Polynomial Graphs Khan Academy Polynomial Graphs Khan Academy Polynomial Graphs Unit – Zeros of Polynomials Unit – + & - Intervals Unit – End Behavior Unit – Put it all together https://www.khanacademy.org/ https://www.khanacademy.org/ https://www.khanacademy.org/ https://www.khanacademy.org/ math/algebra2/ math/algebra2/ math/algebra2/ math/algebra2/ x2ec2f6f830c9fb89:poly-graphs x2ec2f6f830c9fb89:poly-graphs x2ec2f6f830c9fb89:poly-graphs x2ec2f6f830c9fb89:poly-graphs

April 20 April 21 April 22 April 23 April 24 Standard: A2.AAPR.1 Standard: A2.AAPR.1 Standard: A2.AAPR.1 Standard: A2.AAPR.1 Standard: A2.AAPR.1

Learning Tasks: Learning Tasks: Learning Tasks: Learning Tasks: Learning Tasks: Complete 5-1 Study Guide Complete 5-3 Study Guide Operations with Functions – April Standardized Test Practice #1-6 Standardized Test Practice #7-12 22 #1-10

Extension Activities Extension Activities Extension Activities Extension Activities Extension Activities Composing Functions Verifying Inverse Functions https://www.khanacademy.org/ https://www.khanacademy.org/ math/precalculus/ math/precalculus/ x9e81a4f98389efdf:composite x9e81a4f98389efdf:composite

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Algebra 2 Distance Learning Packet

April 27 April 28 April 29 April 30 May 1 Standard: A2.ASE.2 Standard: A2.AREI.2 Standard: A2.AREI.2 Standard: A2.AREI.2 Standard: A2.NCNS.1

Learning Tasks: Learning Tasks: Learning Tasks: Learning Tasks: Learning Tasks: Factor – April 27 #1-8 Solving Equations – April 28 #1-10 Radicals – April 29 #1-10 Rational Exponents – April 30 #1-10 Complex Numbers – May 1 #1-10

Extension Activities Extension Activities Extension Activities Extension Activities Extension Activities Factoring Practice Solving Practice Simplifying Roots Tutorial Fractional Exponents Practice Complex Numbers Tutorial https://www.thatquiz.org/tq- https://www.thatquiz.org/tq-0/?- https://schoolyourself.org https://www.khanacademy.org/math/ https://schoolyourself.org/learn/ 0/?-jh00-l8-mpnv600-p0 j102-l6-mpnv600-p0 /learn/algebra/simplifying-roots algebra2/x2ec2f6f830c9fb89:exp/ precalculus/complex-numbers x2ec2f6f830c9fb89:rational- exp/e/exponents_3

SHG NAME ______DATE ______PERIOD ______

4-4 Study Guide and Intervention Graphing Polynomial Functions

Graphs of Polynomial Functions

If the degree is even and the leading coefficient is positive, then f(x) → +∞ as x → –∞ f(x) → +∞ as x → +∞ If the degree is even and the leading coefficient is negative, then End Behavior of f(x) → –∞ as x → –∞ f(x) → –∞ as x → +∞ Polynomial Functions If the degree is odd and the leading coefficient is positive, then f(x) → –∞ as x → –∞ f(x) → +∞ as x → +∞ If the degree is odd and the leading coefficient is negative, then f(x) → +∞ as x → –∞ f(x) → –∞ as x → +∞ The maximum number of zeros of a polynomial function is equal to the degree of the polynomial. Real Zeros of a A zero of a function is a point at which the graph intersects the x-axis. Polynomial On a graph, count the number of real zeros of the function by counting the number of times Function the graph crosses or touches the x–axis.

Example: Determine whether the graph represents an odd-degree polynomial or an even-degree polynomial. Then state the number of real zeros. As x → –∞, f(x) → –∞ and as x → +∞, f(x) → +∞, so it is an odd-degree polynomial function. The graph intersects the x–axis at 1 point, so the function has 1 real zero.

Exercises For each graph, a. describe the end behavior, b. determine whether it represents an odd-degree or an even-degree function, and c. state the number of real zeroes.

1. 2. 3.

Chapter 4 23 Glencoe Algebra 2 NAME ______DATE ______PERIOD ______

4-4 Word Problem Practice Graphing Polynomial Functions

1. MANUFACTURING A metal sheet is curved 4. DRILLING The volume of a drill bit in cubic according to the shape of the graph of f(x) = 푥4 – 9푥2. millimeters can be estimated by the formula for a 1 What is the degree of this polynomial? cone, V = 휋ℎ푟2, where h is the height in millimeters 3 of the bit and r is its radius in millimeters. 3 Substituting √ r for h, the volume of the drill bit is 3 3 estimated as √ 휋푟3. Graph the function of drill bit 2. GRAPHS Kendra graphed the polynomial f(x) shown 9 below. volume. Describe the end behavior, degree, and sign of the leading coefficient.

From this graph, describe the end behavior, degree, and sign of the leading coefficient. 5. TRIANGLES Dylan drew n dots on a piece of paper making sure that no line contained 3 of the dots. The number of triangles that can be made using the dots as 1 vertices is equal to f(n) = (푛3 – 3푛2 + 2n). 6 3. PENTAGONAL NUMBERS The nth pentagonal 푛(3푛 − 1) number is given by the expression . 2

What is the degree of this polynomial?

What is the seventh pentagonal number?

a. What is the degree of f ?

b. If Dylan drew 15 dots, how many triangles can be made?

Chapter 4 27 Glencoe Algebra 2 NAME ______DATE ______PERIOD ______

4-5 Study Guide and Intervention Analyzing Graphs of Polynomial Functions

Location Principle

Suppose y = f(x) represents a polynomial function and a and b are two numbers such Location Principle that f(a) < 0 and f(b) > 0. Then the function has at least one real zero between a and b.

Example: Determine consecutive integer values of x between which each real zero of f(x) = 2풙ퟒ – 풙ퟑ – 5 is located. Then draw the graph.

Make a table of values. Look at the values of f(x) to locate the zeros. Then use the points to sketch a graph of the function.

x f(x) The changes in sign indicate that there are zeros between x = –2 and x = –1 and between x = 1 and x = 2. –2 35 –1 –2

0 –5 1 –4

2 19

4-5 Study Guide and Intervention (continued) Analyzing Graphs of Polynomial Functions

Maximum and Minimum Points A quadratic function has either a maximum or a minimum point on its graph. For higher degree polynomial functions, you can find turning points, which represent relative maximum or relative minimum points.

Example: Graph f(x) = 풙ퟑ + 6풙ퟐ – 3. Estimate the x-coordinates at which the relative maxima and minima occur. Make a table of values and graph the function.

x f(x) A relative maximum occurs at x = –4 and a relative minimum occurs at x = 0. –5 22 –4 29 ← indicates a relative maximum

–3 24

–2 13 –1 2 ← zero between x = –1, x = 0

0 –3 ←indicates a relative minimum 1 4

2 29

Chapter 4 29 Glencoe Algebra 2 NAME ______DATE ______PERIOD ______

4-5 Skills Practice Analyzing Graphs of Polynomial Functions

Complete each of the following. a. Graph each function by making a table of values. b. Determine the consecutive values of x between which each real zero is located. c. Estimate the x-coordinates at which the relative maxima and minima occur.

1. f(x) = 푥3 – 3푥2 + 1 2. f(x) = 푥3 – 3x + 1

x f(x) x f(x)

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x f(x) x f(x) –3 –1 –2 0 –1 1 0 2 1 3

4 2 5. f(x) = 푥 – 2푥 – 2 6. f(x) = 0.5푥4 – 4푥2 + 4 x f(x) x f(x) –3 –3 –2 –2 –1 –1 0 0 1 1 2 2 3 3

Chapter 4 31 Glencoe Algebra 2

Week 3 Polynomial Project Directions:

1. Choose your assigned function based on the first letter of your last name: 2. Fill out the “Characteristics of a Polynomial Function” graphic organizer. • A-B: 푦 = 2푥3 − 4푥 + 6 • C-D: 푦 = 2푥4 − 4푥2 − 2 3. Write a paragraph detailing all of the key characteristics for the graph to • E-F: 푦 = 2푥4 − 4푥2 − 2푥 include: • G-H: 푦 = −2푥4 + 3푥2 + 1 • type of polynomial function • I-J: 푦 = −2푥3 + 3푥2 + 푥 • domain • K-L: 푦 = −2푥3 + 3푥2 + 푥 − 4 • range • M-N: 푦 = −2푥3 + 푥 − 4 • end behavior • O-Q: 푦 = −2푥2 + 6푥 + 7 • intervals of increase and/or decrease • R-S: 푦 = 3푥2 + 6푥 − 1 • turning points (including whether it’s a relative maximum or relative • T-V: 푦 = 3푥5 + 2푥3 + 푥2 − 푥 − 5 minimum) 1 • W-Z: 푦 = − 푥5 + 3푥2 + 푥 − 5 • zeros and their multiplicity 2 • the effect of the multiplicity on the graph.

NAME ______DATE ______PERIOD ______

5-1 Study Guide and Intervention Operations with Functions

Perform Operations with Functions You can use these rules to perform operations with functions.

Sum (f + g)(x) = f (x) + g(x)

Difference (f – g)(x) = f (x) – g(x)

Product (f ⋅ g)(x) = f (x) ⋅ g(x)

푓 푓(푥) Quotient ( )(x) = , g(x) ≠ 0 푔 푔(푥)

풇 Example: Find (f + g)(x), (f – g)(x), (f ⋅ g)(x), and ( ) (x) for f(x) = 풙ퟐ + 3x – 4 and g(x) = 3x – 2. 품 (f + g)(x) = f(x) + g(x) Addition of functions = (푥2 + 3x – 4) + (3x – 2) f(x) = 푥2 + 3x – 4, g(x) = 3x – 2 = 푥2 + 6x – 6 Simplify. (f – g)(x) = f(x) – g(x) Subtraction of functions = (푥2 + 3x – 4) – (3x – 2) f(x) = 푥2 + 3x – 4, g(x) = 3x – 2 = 푥2 – 2 Simplify. (f ⋅ g)(x) = f(x) ⋅ g(x) Multiplication of functions = (푥2 + 3x – 4)(3x – 2) f(x) = 푥2+ 3x – 4, g(x) = 3x – 2 = 푥2(3x – 2) + 3x(3x – 2) – 4(3x – 2) Distributive Property = 3푥3 – 2푥2 + 9푥2 – 6x – 12x + 8 Distributive Property = 3푥3 + 7푥2 – 18x + 8 Simplify. 푓 푓(푥) ( )(x) = Division of functions 푔 푔(푥) 푥2+ 3푥 − 4 2 = , x ≠ f(x) = 푥2 + 3x – 4 and g(x) = 3x – 2 3푥 − 2 3 Exercises 풇 Find (f + g)(x), (f – g)(x), (f ⋅ g)(x), and ( ) (x) for each f(x) and g(x). 품 1. f(x) = 8x – 3; g(x) = 4x + 5 2. f(x) = 푥2 + x – 6; g(x) = x – 2

3. f(x) = 3푥2 – x + 5; g(x) = 2x – 3 4. f(x) = 2x – 1; g(x) = 3푥2 + 11x – 4

1 5. f(x) = 푥2 – 1; g(x) = 푥 + 1

Chapter 5 5 Glencoe Algebra 2 NAME ______DATE ______PERIOD ______

5-3 Study Guide and Intervention Inverse Functions and Relations

Find Inverses

Two relations are inverse relations if and only if whenever one relation contains the element Inverse Relations (a, b), the other relation contains the element (b, a).

Property of Inverse Suppose f and 푓−1 are inverse functions. Functions Then f(a) = b if and only if 푓−1(b) = a.

ퟐ ퟏ Example: Find the inverse of the function f(x) = x – . Then graph the function and its inverse. ퟓ ퟓ

Step 1 Replace f(x) with y in the original equation. 2 1 2 1 f(x) = x – → y = x – 5 5 5 5

Step 2 Interchange x and y. 2 1 x = y – 5 5

Step 3 Solve for y. 2 1 x = y – Inverse of y = 2 x – 1 5 5 5 5 5x = 2y – 1 Multiply each side by 5. 5x + 1 = 2y Add 1 to each side. 1 (5x + 1) = y Divide each side by 2. 2

2 1 1 The inverse of f(x) = x – is 푓−1(x) = (5x + 1). 5 5 2

Exercises Find the inverse of each function. Then graph the function and its inverse. 2 1 1. f(x) = x – 1 2. f(x) = 2x – 3 3. f(x) = x – 2 3 4

Chapter 5 17 Glencoe Algebra 2

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1) f (x) = x4 + 2x2 - 24 A) f (x) = 2(x - 2)(x + 1)(x2 + 6) B) f (x) = (x - 2)(x + 2)(x2 + 7) C) f (x) = (x + 4)(x + 2)(x2 + 6) D) f (x) = (x - 2)(x + 2)(x2 + 6)

2) f (x) = x6 + 124x3 - 125 A) f (x) = (x + 5)(x2 - 5x + 25)(x - 1)(x2 + x + 1) B) f (x) = (x + 5)(x2 - 5x + 25)(3x - 1)(x2 + x + 1) C) f (x) = (x + 5)(x2 - 5x + 25)(x + 3)(x2 + x + 1) D) f (x) = (x + 5)(x2 - 5x + 25)(x - 1)(x + 1)2

3) f (x) = x4 + 5x3 + 4x2 4) f (x) = x2 + x - 12 A) f (x) = x2(x + 4)(3x + 1) A) f (x) = (x + 4)(x - 3) B) f (x) = 2x2(x + 1)2 B) f (x) = (x + 4)(2x - 3) C) f (x) = x2(x + 4)(x + 1) C) f (x) = 2(x + 2)(x - 3) D) f (x) = x2(x + 4)(3x + 2) D) f (x) = (x + 4)(x + 2)

5) f (x) = x3 - 5x2 + 6x 6) f (x) = x4 - 13x2 + 36 A) f (x) = x(x - 2)(x - 3) A) f (x) = 2(x - 3)(x + 3)(x - 1)(x + 2) B) f (x) = x(x + 3)(x + 5) B) f (x) = (x + 2)2(x + 3)(x - 2) C) f (x) = x(x - 2)(x + 3) C) f (x) = (x + 5)(x + 3)(x - 2)(x + 2) D) f (x) = x(x + 3)(x - 3) D) f (x) = (x - 3)(x + 3)(x - 2)(x + 2)

7) f (x) = x6 + 9x3 + 8 A) f (x) = (x + 1)(x2 + 1)(x + 2)(x2 - 2x + 4) B) f (x) = (x + 2)2(x2 - x + 1)(x2 + x + 6) C) f (x) = (x + 1)(x2 - x + 1)(x + 2)(x2 - 2x + 4) D) f (x) = (x + 1)3(x + 2)(x2 - 2x + 4)

8) f (x) = x3 - 2x2 + 4x - 8 A) f (x) = x(3x2 + 4) B) f (x) = (3x - 2)(x2 + 4) C) f (x) = (x - 2)(x2 + 4) D) f (x) = (x + 1)(x2 + 4)

Worksheet by Kuta Software LLC ©R V2k0c1I9\ vKVuCtKas YS_o_fAt[wRairjeC cLpL\CY.N z `AqlRla lrjixgjhFtXsS prreNsOeUrmvLejdq.^ e dMhaLdWee \wgimtKhR gInnLfuiZnJiItTeH DAclSgEejbmrFai j2D. Algebra 2 Name______ID: 1 ©a [2g0p1w9U RKKugtMal DSbonfUtowXaLrOed pLNLuCG.d h NAJlvlG ]rBiPgDhStkso jrfeYsmeQrzvQeJdK. Solving Equations-April 28 Date______Period____ Solve each equation.

1) -40 - 2a = -8(5 + 7a) 2) 10 + 3x = -4x - (-3 - 8x) A) {-15} B) {0} A) {11} B) {9} C) {-12} D) {5} C) {7} D) {13}

3) -5k - 9 = -2(4k - 6) 4) 2a + 3(1 - 6a) = 29 - 3a A) {-5} B) {7} A) {-1} B) {-3} C) {-8} D) {6} C) {-2} D) {-8}

Find all roots.

5) x3 + 64 = 0 6) x4 - x2 - 42 = 0 A) {-3, 2 + 2i 3, 2 - 2i 3 } A) {i 7, -i 7, i 6, -i 6 } B) {-4, 2 + i 10, 2 - i 10 } B) { 7, - 7, i 3, -i 3 } C) {-4, -1 + i 15, -1 - i 15 } 21 21 C) , - , i 6, -i 6 D) {-4, 2 + 2i 3, 2 - 2i 3 } { 3 3 } D) { 7, - 7, i 6, -i 6 }

7) x3 + 8 = 0 8) x3 - 16x = 0 -3 + i 7 -3 - i 7 A) {0, -4, -3} B) {0, -4, -6} A) -2, , { 2 2 } C) {0, -5, 4} D) {0, -4, 4} B) {-2, 1 + i 3, 1 - i 3 } C) {-2, 1 + i 2, 1 - i 2 } -2 + 2i 2 -2 - 2i 2 D) -2, , { 3 3 }

9) x3 - 2x2 - 37x = 0 10) x4 + 15x2 + 54 = 0 A) {0, 1 + 38, 1 - 38 } A) {2i, -2i, 3i, -3i} B) {0, -1 + 38, -1 - 38 } B) {i 6, -i 6, 3i, -3i} 1 + 4 7 1 - 4 7 C) {i 6, -i 6, i 3, -i 3 } C) 0, , { 3 3 } D) {i 3, -i 3, 3i, -3i} D) {0, 1 + i 38, 1 - i 38 }

Worksheet by Kuta Software LLC ©N q2U0l1`9N YK^ustTaf hSNobfDtJwYavrseJ oLpLlCU.Z t GA`lPl[ DrGifgshNt\sO YrqeisJekriv\eWdg.^ ^ hM^agdWey [waiYtzhP NIMnbfuiunfiUtSei cAFlsgce_b[rfay L2^. Algebra 2 Name______ID: 1 ©i s2P0t1m9Z jKduFtlaf uSSorfktvwMaxr`ey \LbLzCi.B X yA^l^lY PrciIgBhMtpsc GrfeGsnedrzvSewdv. Radicals-April 29 Date______Period____ Simplify.

1) -3 24 + 3 54 + 3 5 2) -3 3 - 3 3 + 2 12 A) 3 6 + 3 5 B) 18 6 A) -2 3 B) 3 3 C) 9 6 + 3 5 D) 9 6 C) - 3 D) -5 3

3) -5 3( 6 + 5) 4) 15( 10 - 3 6) A) 7 5 A) 5 6 - 9 10 B) 4 5 - 10 2 B) 4 3 - 12 C) 9 5 + 5 2 C) 3 30 + 2 D) -15 2 - 25 3 D) 54

Solve each equation. Remember to check for extraneous solutions.

5) 5v = 4v + 1 6) x = 2x - 6 A) {-9} B) {-2} A) {-1} B) {6} C) {-9, 2} D) {1} C) No solution. D) {-1, 6}

7) m = 12 - m 8) 12 = 10 + x + 4 A) {-6} B) {10} A) {-7} B) {0} C) {-10} D) {6} C) {1} D) {-2, 0}

9) n = 3 + 2n 10) x = 72 - x A) {3, -8} B) {-9, -1} A) {8} B) {-3, 4} C) {3} D) {3, -1} C) {-3, 8} D) {8, -9}

Worksheet by Kuta Software LLC ©o x2g0Q1z9b rKJuKtBaX XSYolfWtfwlaurzeY _L[LECy.N i nARlIle HreiXgnhQtUsw YrgejsFeArpvIeBdC.t q nMtapdMe[ cwpiztthu xIPnYfniVnii^tzej FA_lDg`eHbzrEaj v2Z. Algebra 2 Name______ID: 1 ©H F2v0S1z9f \KeudtXak JSzoafntYwsa^r^eJ FLjLbCd.z x WAflylI WrEi`gLhqtdsR [rZeisXeqrCvgeOd_. Rational Exponents-April 30 Date______Period____ Write each expression in radical form.

7 3 1) (5x) 4 2) k 4 4 5 4 7 4 5 3 A) ( x) B) ( 5x) A) ( 3k) B) ( k) 3 2 3 4 3 5 7 C) ( 4x) D) x2 C) ( k) D) ( k)

3 1 3) (10x) 2 4) (4x) 3 4 7 3 4 3 3 2 A) ( 3x) B) ( x) A) 4x B) ( 4x) 3 3 C) ( 3x) D) ( 10x) C) x D) 6x

Write each expression in exponential form.

1 6 7 5) 6) ( 10) 5 ( 2) 7 1 6 2 1 5 A) 10 B) 7 3 3 5 7 A) 5 B) 5 - 2 6 5 4 - C) 7 D) 10 C) 2 2 D) 7 3

Solve each equation.

3 3 7) -8 + x 4 = 0 8) -1 + x 2 = 26 A) {-16, -5} B) {-16, 5} A) {-3} B) {12, -3} C) {16, -5} D) {16} C) {9} D) {-3, -5}

4 9) -4 = -2 a 5 10) -2 - k 3 = -1026 A) {16} B) {5, 4} C) {4} D) {-11, 4} A) {64, -7} B) {26, -7} C) {26, 11} D) {64}

Worksheet by Kuta Software LLC ©r q2u0o1S9\ iKvumtIax USOoLfStHwXaUr_eV FLFLvCj.D u MA\lOlu SrviAgXhXtTsk krveEsDeGrcvCendx.C T VMVaRdNen pwuittKhS bImnFfiiEnMittjez uAHlugve[bMrgai `2c. Algebra 2 Name______ID: 1 ©i j2A0[1j9] TKZu^tda` OSToZfUtewAazrreh ZLjLcCC.r K lAClYlv ArpiWgLhXtKsl zrKemsxeXrevSeQdB. Complex Numbers-May 1 Date______Period____ Simplify.

1) (-3 - 4i)2 2) (2 + 2i) - (-4 + 4i) A) -7 + 24i B) 49 A) 6 - 2i B) -6 - 6i C) 64 D) -7 - 24i C) 6 + 6i D) 3 - 2i

3) -7 + (3 - 8i) - 6 4) (-3 + 3i) - (-8 + 5i) A) 2 - 8i B) -19 A) 5 + 2i B) 5 + 8i C) -10 + 8i D) -10 - 8i C) 2 + i D) 5 - 2i

5) (-4 + 4i) - (-4 + 3i) 6) (-6 - 8i)(8 + 4i) A) -3 + 4i B) i A) -195 B) -80 + 40i C) 7i D) -2 + i C) 80 - 40i D) -16 - 88i

7) (8 + 7i) + (3 - 2i) 8) (-8 + 7i) - (8 - 7i) A) 5 + 9i B) 9 + 5i A) -16 + 14i B) -9 + 7i C) 5 + 5i D) 11 + 5i C) -16 D) -14 + 14i

4 5 9) - 10) 2i 2i 7i i 5i A) B) A) -2i B) - 2 2 2 3i 5i C) 2i D) C) -i D) - 2 7

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