Answers. Chapter Start Thinking Sample answer: y-intercept: 8 5. x x
|
|
- Erik Flynn
- 5 years ago
- Views:
Transcription
1 . ( 7, ) 9. (, 9 ) 0. (, 7). no solution. (, 7). no solution. no solution. ( 7, ). infinitel man solutions 7. (, 7 ). infinitel man solutions 9. (, 9) 70. 9a + a + 7. b b c + 90c d d + 7. m m + 7. n + n q q intercept:, -intercept: 79. -intercept:, -intercept: 0. -intercept: 7, -intercept: 7. -intercept:, -intercept:. -intercept:, -intercept:. -intercept: 9, -intercept: p 0 p g( ) + 9. g( ) + 9. g( ) + 9. g( ) + 9. infinitel man solutions 97. (,, 7 ) 9. infinitel man solutions 99. no solution 00. (,, ) 0. (,, 7) 0. in. b in. 0. a. You need 7. pounds of peanuts,. pounds of raisins,. pounds of pretzels, and pounds of chocolate cand pieces. b. Recipe B c. lbs 0. our friend; $.0 Chapter. Start Thinking Sample answer: f ( ) 0 f( ) 0 f( ) ( ) 0 f( ) 9 0 f ( ) f 0 f( ) 0 ( ) + 0 f( ) + The function f( ) ( ) is a horizontal translation unit right ( h ). The function f ( ) ( ) is a vertical stretch b a factor of ( a ). The function f( ) + is a vertical translation unit up ( k ). Copright Big Ideas Learning, LLC Algebra A9
2 . Warm Up a + a. The graph of g is a translation units right of the f() Cumulative Review Warm Up. g ( ) +. g ( ). g ( ). Practice A. The graph of g is a translation units down of the g() ( ). The graph of g is a translation units left and unit down of the f() f() g() ( + ) g(). The graph of g is a translation unit up of the g() + f(). The graph of g is a translation unit left of the g() ( + ) 7. The graph of g is a reflection in the -ais followed b a vertical stretch b a factor of of the graph of f. f(). The graph of g is a reflection in the -ais followed b a horizontal shrink of the graph of f b a factor of. g() ( ) g() f(). The graph of g is a translation units right of the f() f() 9. The graph of g is a vertical shrink b a factor of of the f() g() g() ( ) A0 Algebra Copright Big Ideas Learning, LLC
3 0. When 0 < a < in the function g( ) a f( ), the transformation is a vertical shrink, not stretch; The graph of g is a reflection in the -ais followed b a vertical shrink b a factor of of the graph of the parent quadratic function.. The graph is a vertical stretch b a factor of, followed b a translation units left and units up of the parent quadratic function; (, ). The graph is a reflection in the -ais, followed b a vertical stretch b a factor of and a translation unit down of the parent quadratic function; (0, ). g ( ) ; (0, ). The graph of g is a translation unit right and units up of the g() ( ) +. The graph of g is a translation units right and units up of the f(). g ( ) 7; (0, 7) g() ( ) +. a. b. a h k g,, ; ( ) ( ) a h k g. Practice B,, ; ( ) ( ). The graph of g is a translation units up of the f(). The graph of g is a translation units left and units down of the g() + f() f(). The graph of g is a translation units left of the g() ( + ) 7. The graph of g is a reflection in the -ais, followed b a horizontal stretch b a factor of of the graph of f. f() f() ( ) g() g() ( + ). The graph of g is a translation units left and units down of the f(). The graph of g is a vertical shrink b a factor of, followed b a translation units up of the graph of f. g() + g() ( + ) f() Copright Big Ideas Learning, LLC Algebra A
4 9. The graph of g is a vertical shrink b a factor of, followed b a translation unit left of the graph of f. f() g() ( + ) 0. The graph is a reflection in the -ais, followed b a vertical stretch b a factor of and a translation units left and units down of the parent quadratic function; (, ). The graph is a vertical shrink b a factor of, followed b a translation units right and unit up of the parent quadratic function; (, ). Start Thinking 0 f( ) 0 V shape; es; es; The line of smmetr is the -ais.. Warm Up f(). P (, ). P (, ). P (, ). P (, ). Cumulative Review Warm Up. linear; ; 0; After jogging for 0 minutes, 0 calories were burned.. ( + ) g ( ) ; (, 0). g ( ) (+ ) ; (, ). h ( ) f( ) + Add to the output. + Substitute ( ). Enrichment and Etension ; ( ) ; ( ) ; + ( ) ; ( ) ; ( ) ; ( ) f and simplif. g( ) h( ) Multipl the input b. into h ( ) and simplif. + + Substitute. not linear. Practice A.. f() ( ) (, 0).. g() ( + ) + (, ) f() ( + ) (, 0) h() ( ) (, ). Puzzle Time EL SALVADOR. ( ) + (, ) A Algebra Copright Big Ideas Learning, LLC
5 .. f() ( + ) (, ) 0 f() (0, ) 7.. Both graphs have the same ais of smmetr, (, ) (, 0) + + (, 7) + +. C; It has the largest leading coefficient, a.. minimum: ; domain: all real numbers, range: ; increasing to the right of 0; decreasing to the left of 0. minimum: ; domain: all real numbers, range: ; increasing to the right of 0; decreasing to the left of 0 7. maimum: ; domain: all real numbers, range: ; increasing to the left of ; decreasing to the right of. maimum: ; domain: all real numbers, range: ; increasing to the left of ; decreasing to the right of 9. a. noon b. 7 customers. Practice B 0. (, ) f() +.. (, ) f() ( + ) + (, ) f() ( ). 0 g() + (0, ).. (, ) g() ( + ) + (, ) h() ( ) Copright Big Ideas Learning, LLC Algebra A
6 cm 7 in.. 0.( ) 7. maimum: ; domain: all real numbers, range: ; increasing to the left of ; decreasing to the right of. (, 0) f() 0.. minimum:.; domain: all real numbers, range:.; increasing to the right of ; decreasing to the left of 9. a. The maimum height occurs mile from the base of the bridge. 0 (0, ) b. The maimum height is mile. 7.. (0, ) (0, ) 0. Enrichment and Etension f() no; The definition of a quadratic function sas a 0, but for the ais of smmetr to be undefined, a would have to be 0... (, ) + (,.). lowest; The -values on either side of are greater than.. A; Both have an ais of smmetr of.. minimum: ; domain: all real numbers, range: ; increasing to the right of 0; decreasing to the left of 0. maimum: 9; domain: all real numbers, range: 9; increasing to the left of ; decreasing to the right of (,.) (, ) f(). Sample answer: (,0); The -value 7 is units awa from the verte -value. Because the -value is also units awa from, it has the same output value 0.. Puzzle Time THIS BRITISH ROWER WAS THE FIRST WOMAN TO ROW ACROSS THREE OCEANS.. Start Thinking Sample answer: D(, ) C(, ) cm 7 B(, ) P ( 0, in. ( A(, ) es; Point P is the same distance from the parabola as the line is to the parabola. So, it will alwas ield the same distance as long as the measurement is taken from a point on the graph of the parabola. A Algebra Copright Big Ideas Learning, LLC
7 . Warm Up Cumulative Review Warm Up z 0. z... Practice A A; The directri is below the focus.. focus: (0, ), directri:, ais of smmetr: 0. in.; The receiver is at the focus verte: (, ), focus: (, ), directri: 0, ais of smmetr: ; The graph is a vertical shrink b a factor of, followed b a translation unit right and units up. 9. verte: (, ), focus: (, ), directri: 0, ais of smmetr: ; The graph is a vertical shrink b a factor of, followed b a reflection in the -ais and a translation units left and units down. 0. verte: (, ), focus: (, ), directri:, ais of smmetr: ; The graph is a translation units right and units down.. verte: (, 0), focus: (, ), directri: 7, ais of smmetr: ; The graph is a vertical shrink b a factor of, followed b a reflection in 7 the -ais and a translation units left and 0 units up. 9. focus: (0, ), directri:, ais of smmetr: 0. Practice B focus: (0, ), directri:, ais of smmetr: 0 0. focus: (, 0), directri:, ais of smmetr: 0 Copright Big Ideas Learning, LLC Algebra A
8 . focus: (, 0), directri:, ais of smmetr: focus: (, 0), directri:, ais of smmetr: 0 0. focus: (0, 9), directri: 9, ais of smmetr: 0 0,, directri: ais of smmetr: 0. focus: ( ) 0,, directri:, ais of smmetr: 0. focus: ( ) 0 + 0,. verte: (, ), focus: ( 7, ), directri:, ais of smmetr: ; The graph is a shrink towards the -ais b a factor of, followed b a reflection in the -ais and a translation units left and units up.. verte: ( ) (, ), focus:,, directri:, ais of smmetr: ; The graph is a vertical stretch b a factor of, followed b a translation units left and unit down.. verte: 9 ( ) (, ), focus:,, directri:, 0 0 ais of smmetr: ; The graph is a stretch awa from the -ais b a factor of 0, followed b a translation units right and units down.. verte: (, 9), focus: (, ), directri: 7, ais of smmetr: ; The graph is a vertical shrink b a factor of, followed b a reflection in the -ais and a translation unit left and 9 units up.. Enrichment and Etension.. a. b.. RS has a slope of n n s r ( s r)( s + r) s + r r + s. s r s r t 0 t OT has a slope of t. t 0 t Because RS and OT are parallel lines, their slopes are equal. So, r + s t. A Algebra Copright Big Ideas Learning, LLC
9 . To find the midpoint of a line segment, find the average of the -values and -values of the endpoints. The -value of the midpoint of RS would be r + s. t The -value of the midpoint OT would be. u + v The -value of the midpoint UV would be. UV has as slope of v u ( v u)( v + u) v + u u + v. v u v u Because UV is parallel to both RS and OT, all slopes are equal and u + v r + s t. So, the -values of their midpoints are all the same t r + s and lie on the same line, or or u + v.. Puzzle Time YELLOWSTONE PARK. Start Thinking Sample answer: 0.; After weeks, ou have $0. in our bank account.. Warm Up. ( ). ( ). + ( ). + ( ) + ( ). + ( ). Mone in bank account 0 0 Your Checking Account Weeks. Cumulative Review Warm Up.... The graph is a vertical stretch b a factor of, followed b a translation unit down of its parent function. The graph is a vertical stretch b a factor of, followed b a reflection in the -ais of its parent function. The graph is a vertical stretch b a factor of, followed b a translation 7 units up of its parent function. The graph is a reflection in the -ais, followed b a translation units right and unit down.. Practice A.. f() h() g() 0 f() 0 7 ( ). ( ) 9( + ) +. ( 0)( ). ( )( ). 7 ( + )( + ) 0 0 f() f() ( ) h() g() Copright Big Ideas Learning, LLC Algebra A7
10 7. a. b. 9 ( ) c. 9 ( + )( ) d e. es; intercept form; Two intercepts were given.. 9. ft. Practice B. ( ) ( ) +. ( )( ). ( + 7)( + ). ( 9)( 9) ( ) 7. The two given sets of coordinates were not substituted into the correct places. 7 a ( h) a( ) + k 7 a a a The equation is ( ).. a. The maimum area of 00 square feet occurs when the length is 0 feet. b. A ( ) + 00 ; A() 9 ft c. 0 to 0 ft: ft 0 ; 0 to 00 ft: ft. Enrichment and Etension. linear; quadratic a b. +.9( ) 7. ft 0 ft c. The graph of the function is a reflection in the -ais, followed b a vertical stretch b a factor of.9 and a translation units right and 7. units up of its parent function.. quadratic a b. + ( ) 7 c. The graph of the function is a reflection in the -ais, followed b a vertical stretch b a factor of and a translation units right and 7 units up of its parent function.. linear; quadratic a. + + b. + (.). c. The graph of the function is a reflection in the -ais, followed b a vertical stretch b a factor of and a translation. units right and. units up of its parent function.. Puzzle Time PINK FLAMINGO Cumulative Review a. 9% b. 9% c. correct answers d. 0 correct answers. a. 9% b. 7% c. correct answers d. correct answers e. correct answers 9. cups 0. tablespoons A Algebra Copright Big Ideas Learning, LLC
11 or no solution. no solution 7. no solution ( )( + 7). ( + )( + ) 9. ( + )( ) 90. ( )( + ) 9. ( + )( ) 9. ( )( ) 9. ( + )( + ) 9. ( )( ) 9. ( + )( + ) 9. ( + 7)( ) 97. ( + 0)( ) 9. ( )( + 0) 99. ( )( 0) 00. ( )( + ) 0. ( )( + ) 0. ( )( + ) 0. ( + 9)( 9) 0. ( + 0)( ) or ( )( + ) no solution. h 7.. h. about. h ( + )( ). ( + )( 7). ( )( + ) Copright Big Ideas Learning, LLC Algebra A9
12 . in.. ft. in... in. 7. ± i f(). ± 9. ± 7 h() The graph of h ( ) is a vertical shrink b a factor 0. ± i 7 of and a reflection in the -ais of the graph of f ( ).. ± 0. ± ± 9. 7 ± 9. ± i 7 ± i 9 f() c() 7. 7 ± i 7. ± i 7 The graph of c ( ) is a vertical translation units down of the graph of f ( ). 9. ± i 0. ± i ± i. ± i d() f(). ±. ± i The graph of d( ) is a vertical stretch b a factor of of the graph of f ( ).. 9 ± 0. ± i. 7. f() f() k() + g() The graph of g( ) is a vertical stretch b a factor of of the graph of f ( ). The graph of k ( ) is a horizontal translation units left of the graph of f ( ).. The graph of m ( ) is a translation units right and units up of the graph of f ( ). m() + f() A0 Algebra Copright Big Ideas Learning, LLC
13 . g ( ). g ( ) 7 +. g( ) + +. g ( ) 7 7. g( ). g( ) g ( ) 0. g ( ) +. no solution.,. (, ) or about ( 0.7,.9). Cumulative Review Warm Up. f() ( + ) Chapter. Start Thinking (, 0). g() ( ) (, ) Equation Number of -intercepts Point(s) ( 0, 0 ) ( 0, 0 ) (, 0 ), (, 0) 0 N/A.. (, ) ( + ) f() + (0, ) Yes, there are patterns; Sample answer: A quadratic equation has one -intercept when the verte is on the -ais. If the quadratic equation opens down, the graph has two -intercepts if the constant is positive and none if the constant is negative. If the quadratic equation opens up, the graph has two -intercepts if the constant is negative and none if the constant is positive; The verte is a minimum if the term is positive; The verte is a maimum if the term is negative.. Warm Up. (, ). (, ). infinitel man solutions. Practice A 0. and.. and. and. and. and Copright Big Ideas Learning, LLC Algebra A
Answers. Chapter Warm Up. Sample answer: The graph of h is a translation. 3 units right of the parent linear function.
Chapter. Start Thinking As the string V gets wider, the points on the string move closer to the -ais. This activit mimics a vertical shrink of a parabola... Warm Up.. Sample answer: The graph of f is a
More informationAnswers. Chapter Warm Up. Sample answer: The graph of f is a translation 3 units right of the parent linear function.
Chapter. Start Thinking As the string V gets wider, the points on the string move closer to the -ais. This activit mimics a vertical shrink of a parabola... Warm Up.. Sample answer: The graph of f is a
More information4. exponential decay; 20% 9.1 Practice A found square root instead of cube root 16 =
9.. eponential deca; 0% 9. Practice A.. 7. 7.. 6. 9. 0 7.. 9. 0. found square root instead of cube root 6 = = = 9. = 7, 9. =,.. 7n 7n. 96. =, 97. =, 9. linear function: = + 0 99. quadratic function: =
More information3.6 Start Thinking. 3.6 Warm Up. 3.6 Cumulative Review Warm Up. = 2. ( q )
.6 Start Thinking Graph the lines = and =. Note the change in slope of the line. Graph the line = 0. What is happening to the line? What would the line look like if the slope was changed to 00? 000? What
More informationMaintaining Mathematical Proficiency
Name Date Chapter 8 Maintaining Mathematical Proficienc Graph the linear equation. 1. = 5. = + 3 3. 1 = + 3. = + Evaluate the epression when =. 5. + 8. + 3 7. 3 8. 5 + 8 9. 8 10. 5 + 3 11. + + 1. 3 + +
More information5.2 Start Thinking Sample answer: x the cost of an incandescent light bulb, y the cost of a CFL, 30x 2 3 3, t 25; t 6F
5.1 Cumulative Review Warm Up. y 5 5 8 1. y 1. y 1 4 8 4. y 5 4 5 5. y 5 4 6. y 5 7. y 1 8 8. y 7 5.1 Practice A 4 5 1. yes. no., 0 4., 4 5., 6 6., 5 7. 8, 8. 0.67,.5 9. 16 bracelets, 1 necklaces 10. y
More information3.7 Start Thinking. 3.7 Warm Up. 3.7 Cumulative Review Warm Up
.7 Start Thinking Use a graphing calculator to graph the function f ( ) =. Sketch the graph on a coordinate plane. Describe the graph of the function. Now graph the functions g ( ) 5, and h ( ) 5 the same
More information3.1 Start Thinking. 3.1 Warm Up. 3.1 Cumulative Review Warm Up. Consider the equation y = x.
3.1 Start Thinking Consider the equation =. Are there an values of that ou cannot substitute into the equation? If so, what are the? Are there an values of that ou cannot obtain as an answer? If so, what
More informationMaintaining Mathematical Proficiency
Chapter Maintaining Mathematical Proficienc Find the -intercept of the graph of the linear equation. 1. = + 3. = 3 + 5 3. = 10 75. = ( 9) 5. 7( 10) = +. 5 + 15 = 0 Find the distance between the two points.
More informationWriting Quadratic Functions in Standard Form
Chapter Summar Ke Terms standard form (general form) of a quadratic function (.1) parabola (.1) leading coefficient (.) second differences (.) vertical motion model (.3) zeros (.3) interval (.3) open interval
More information2.3 Start Thinking. 2.3 Warm Up. 2.3 Cumulative Review Warm Up
. Start Thinking Choose an two numbers and compare them with an inequalit smbol ( < or > ). Multipl each number b 1. Is the new inequalit still true? Continue this eercise b dividing the original inequalit
More informationLesson Goals. Unit 4 Polynomial/Rational Functions Quadratic Functions (Chap 0.3) Family of Quadratic Functions. Parabolas
Unit 4 Polnomial/Rational Functions Quadratic Functions (Chap 0.3) William (Bill) Finch Lesson Goals When ou have completed this lesson ou will: Graph and analze the graphs of quadratic functions. Solve
More informationQuadratic Functions Objective: To be able to graph a quadratic function and identify the vertex and the roots.
Name: Quadratic Functions Objective: To be able to graph a quadratic function and identif the verte and the roots. Period: Quadratic Function Function of degree. Usuall in the form: We are now going to
More informationQuadratic Function. Parabola. Parent quadratic function. Vertex. Axis of Symmetry
Name: Chapter 10: Quadratic Equations and Functions Section 10.1: Graph = a + c Quadratic Function Parabola Parent quadratic function Verte Ais of Smmetr Parent Function = - -1 0 1 1 Eample 1: Make a table,
More informationFor questions 5-8, solve each inequality and graph the solution set. You must show work for full credit. (2 pts each)
Alg Midterm Review Practice Level 1 C 1. Find the opposite and the reciprocal of 0. a. 0, 1 b. 0, 1 0 0 c. 0, 1 0 d. 0, 1 0 For questions -, insert , or = to make the sentence true. (1pt each) A. 5
More informationChapter 10 Answers. Practice (0,0); maximum 2. (0,0); maximum 3. (0,0); minimum y = x 2, y = 3x 2, y = 5x 2 8. y 1
Chapter 0 Answers Practice 0-. (0,0); maimum. (0,0); maimum. (0,0); minimum. (0,0); minimum. (0,0); maimum. (0,0); minimum 7. =, =, =. =, =-, =-. =, =-, = 0. =, =, =-. =, =, =-7. =, =, =........ 7. 0 7...
More informationMaintaining Mathematical Proficiency
Name Date Chapter 3 Maintaining Mathematical Proficienc Plot the point in a coordinate plane. Describe the location of the point. 1. A( 3, 1). B (, ) 3. C ( 1, 0). D ( 5, ) 5. Plot the point that is on
More informationName Date. Work with a partner. Each graph shown is a transformation of the parent function
3. Transformations of Eponential and Logarithmic Functions For use with Eploration 3. Essential Question How can ou transform the graphs of eponential and logarithmic functions? 1 EXPLORATION: Identifing
More information5.7 Start Thinking. 5.7 Warm Up. 5.7 Cumulative Review Warm Up
.7 Start Thinking Graph the linear inequalities < + and > 9 on the same coordinate plane. What does the area shaded for both inequalities represent? What does the area shaded for just one of the inequalities
More informationC H A P T E R 3 Polynomial Functions
C H A P T E R Polnomial Functions Section. Quadratic Functions and Models............. 9 Section. Polnomial Functions of Higher Degree......... Section. Polnomial and Snthetic Division............ 8 Section.
More informationSample Questions to the Final Exam in Math 1111 Chapter 2 Section 2.1: Basics of Functions and Their Graphs
Sample Questions to the Final Eam in Math 1111 Chapter Section.1: Basics of Functions and Their Graphs 1. Find the range of the function: y 16. a.[-4,4] b.(, 4],[4, ) c.[0, ) d.(, ) e.. Find the domain
More information= x. Algebra II Notes Quadratic Functions Unit Graphing Quadratic Functions. Math Background
Algebra II Notes Quadratic Functions Unit 3.1 3. Graphing Quadratic Functions Math Background Previousl, ou Identified and graphed linear functions Applied transformations to parent functions Graphed quadratic
More information4.2 Start Thinking. 4.2 Warm Up. 4.2 Cumulative Review Warm Up
. Start Thinking How can ou find a linear equation from a graph for which ou do not know the -intercept? Describe a situation in which ou might know the slope but not the -intercept. Provide a graph of
More informationFair Game Review. Chapter 8. Graph the linear equation. Big Ideas Math Algebra Record and Practice Journal
Name Date Chapter Graph the linear equation. Fair Game Review. =. = +. =. =. = +. = + Copright Big Ideas Learning, LLC Big Ideas Math Algebra Name Date Chapter Fair Game Review (continued) Evaluate the
More informationAnswers. Chapter 4 A15
. =. Sample answer:. a. B is congruent to itself. A and D have the same line of sight, and so the are congruent. Because two angles are congruent, the third angles are congruent. Because the triangles
More information3.5 Start Thinking. 3.5 Warm Up. 3.5 Cumulative Review Warm Up
3.5 Start Thinking Tractor-trailers often weigh in ecess of 50,000 pounds. With all the weight on board, these trucks need an etra warning when traveling down steep hills. Research the term roadway grade
More informationMATH 115: Final Exam Review. Can you find the distance between two points and the midpoint of a line segment? (1.1)
MATH : Final Eam Review Can ou find the distance between two points and the midpoint of a line segment? (.) () Consider the points A (,) and ( 6, ) B. (a) Find the distance between A and B. (b) Find the
More informationFinal Exam Review Part 2 #1 Page 1 / 21
Final Eam Review Part #1 Intermediate Algebra / MAT 135 Spring 017 Master ( Master Templates) Student Name/ID: v 1. Solve for, where is a real number. v v + 1 + =. Solve for, where is a real number. +
More informationReady To Go On? Skills Intervention 10-1 Introduction to Conic Sections
Find this vocabular word in Lesson 10-1 and the Multilingual Glossar. Graphing Parabolas and Hperbolas on a Calculator A is a single curve, whereas a has two congruent branches. Identif and describe each
More informationName K ^2u0g1U7d pkhutt[ad nsqojfctrwlatraep klylect.r _ ma]lulm yruibg^hxttst mrne\sue]rvveerdj. 2) h(n) = -n 2-3n; Find h(n - 2) -n 2 + n + 2
Advanced Algebra II Name K ^u0gu7d pkhutt[ad nsqojfctrwlatraep klylect.r _ ma]lulm ruibg^httst mrne\sue]rvveerdj. Semester Review Evaluate each function. ) w() = - + ; Find w(-7) ) h(n) = -n - n; Find
More informationName Date. and y = 5.
Name Date Chapter Fair Game Review Evaluate the epression when = and =.... 0 +. 8( ) Evaluate the epression when a = 9 and b =.. ab. a ( b + ) 7. b b 7 8. 7b + ( ab ) 9. You go to the movies with five
More informationMathematics 10 Page 1 of 7 The Quadratic Function (Vertex Form): Translations. and axis of symmetry is at x a.
Mathematics 10 Page 1 of 7 Verte form of Quadratic Relations The epression a p q defines a quadratic relation called the verte form with a horizontal translation of p units and vertical translation of
More informationa [A] +Algebra 2/Trig Final Exam Review Fall Semester x [E] None of these [C] 512 [A] [B] 1) Simplify: [D] x z [E] None of these 2) Simplify: [A]
) Simplif: z z z 6 6 z 6 z 6 ) Simplif: 9 9 0 ) Simplif: a a a 0 a a ) Simplif: 0 0 ) Simplif: 9 9 6) Evaluate: / 6 6 6 ) Rationalize: ) Rationalize: 6 6 0 6 9) Which of the following are polnomials? None
More informationReview Exercises for Chapter 2
Review Eercises for Chapter 7 Review Eercises for Chapter. (a) Vertical stretch Vertical stretch and a reflection in the -ais Vertical shift two units upward (a) Horizontal shift two units to the left.
More informationNAME DATE PERIOD. Study Guide and Intervention. Transformations of Quadratic Graphs
NAME DATE PERID Stud Guide and Intervention Write Quadratic Equations in Verte Form A quadratic function is easier to graph when it is in verte form. You can write a quadratic function of the form = a
More informationAnswers Investigation 2
Applications 1. a. Square Side Area 4 16 2 6 36 7 49 64 9 1 10 100 11 121 Rectangle Length Width Area 0 0 9 1 9 10 2 20 11 3 33 12 4 4 13 6 14 6 4 1 7 10 b. (See Figure 1.) c. The graph and the table both
More informationUnit 10 - Graphing Quadratic Functions
Unit - Graphing Quadratic Functions PREREQUISITE SKILLS: students should be able to add, subtract and multipl polnomials students should be able to factor polnomials students should be able to identif
More informationRELATIONS AND FUNCTIONS through
RELATIONS AND FUNCTIONS 11.1.2 through 11.1. Relations and Functions establish a correspondence between the input values (usuall ) and the output values (usuall ) according to the particular relation or
More informationEOC Review. Algebra I
EOC Review Algebra I Order of Operations PEMDAS Parentheses, Eponents, Multiplication/Division, Add/Subtract from left to right. A. Simplif each epression using appropriate Order of Operations.. 5 6 +.
More informationGlossary. Also available at BigIdeasMath.com: multi-language glossary vocabulary flash cards. An equation that contains an absolute value expression
Glossar This student friendl glossar is designed to be a reference for ke vocabular, properties, and mathematical terms. Several of the entries include a short eample to aid our understanding of important
More informationMath 121. Practice Questions Chapters 2 and 3 Fall Find the other endpoint of the line segment that has the given endpoint and midpoint.
Math 11. Practice Questions Chapters and 3 Fall 01 1. Find the other endpoint of the line segment that has the given endpoint and midpoint. Endpoint ( 7, ), Midpoint (, ). Solution: Let (, ) denote the
More informationPRACTICE FINAL EXAM. 3. Solve: 3x 8 < 7. Write your answer using interval notation. Graph your solution on the number line.
MAC 1105 PRACTICE FINAL EXAM College Algebra *Note: this eam is provided as practice onl. It was based on a book previousl used for this course. You should not onl stud these problems in preparing for
More informationChapter 5: Quadratic Equations and Functions 5.1 Modeling Data With Quadratic Functions Quadratic Functions and Their Graphs
Ch 5 Alg Note Sheet Ke Chapter 5: Quadratic Equations and Functions 5.1 Modeling Data With Quadratic Functions Quadratic Functions and Their Graphs Definition: Standard Form of a Quadratic Function The
More informationChapter Summary. How does Chapter 10 fit into the BIGGER PICTURE of algebra?
Page of 5 0 Chapter Summar WHAT did ou learn? Find the distance between two points. (0.) Find the midpoint of the line segment connecting two points. (0.) Use distance and midpoint formulas in real-life
More informationCollege Algebra ~ Review for Test 2 Sections
College Algebra ~ Review for Test Sections. -. Use the given graphs of = a + b to solve the inequalit. Write the solution set in interval notation. ) - + 9 8 7 6 (, ) - - - - 6 7 8 - Solve the inequalit
More informationLesson 9.1 Using the Distance Formula
Lesson. Using the Distance Formula. Find the eact distance between each pair of points. a. (0, 0) and (, ) b. (0, 0) and (7, ) c. (, 8) and (, ) d. (, ) and (, 7) e. (, 7) and (8, ) f. (8, ) and (, 0)
More informationAttributes and Transformations of Quadratic Functions VOCABULARY. Maximum value the greatest. Minimum value the least. Parabola the set of points in a
- Attributes and Transformations of Quadratic Functions TEKS FCUS VCABULARY TEKS ()(B) Write the equation of a parabola using given attributes, including verte, focus, directri, ais of smmetr, and direction
More informationKCATM 2013 Algebra Team Test. E) No Solution. C x By. E) None of the Above are correct C) 9,19
KCTM 03 lgebra Team Test School ) Solve the inequality: 6 3 4 5 5 3,,3 3, 3 E) No Solution Both and B are correct. ) Solve for : By C C B y C By B C y C By E) None of the bove are correct 3) Which of the
More informationAlgebra 2 Semester Exam Review
Algebra Semester Eam Review 7 Graph the numbers,,,, and 0 on a number line Identif the propert shown rs rs r when r and s Evaluate What is the value of k k when k? Simplif the epression 7 7 Solve the equation
More informationAnswers. Chapter 4 A33. + as. 4.1 Start Thinking
. + 7i. 0 i 7. 9 i. 79 + i 9. 7 i 0. 7 i. + i. 0 + i. a. lb b. $0. c. about $0.9 Chapter. Start Thinkin () = () = The raph o = is a curv line that is movin upward rom let to riht as increases. The raph
More informationChapter 2 Polynomial, Power, and Rational Functions
Section. Linear and Quadratic Functions and Modeling 6 Chapter Polnomial, Power, and Rational Functions Section. Linear and Quadratic Functions and Modeling Eploration. $000 per ear.. The equation will
More information1. Find the domain of the following functions. Write your answer using interval notation. (9 pts.)
MATH- Sample Eam Spring 7. Find the domain of the following functions. Write your answer using interval notation. (9 pts.) a. 9 f ( ) b. g ( ) 9 8 8. Write the equation of the circle in standard form given
More informationMt. Douglas Secondary
Foundations of Math 11 Section 7.1 Quadratic Functions 31 7.1 Quadratic Functions Mt. Douglas Secondar Quadratic functions are found in everda situations, not just in our math classroom. Tossing a ball
More informationCHAPTER 3 Polynomial Functions
CHAPTER Polnomial Functions Section. Quadratic Functions and Models............. 7 Section. Polnomial Functions of Higher Degree......... 7 Section. Polnomial and Snthetic Division............ Section.
More informationName Class Date. Deriving the Standard-Form Equation of a Parabola
Name Class Date 1. Parabolas Essential Question: How is the distance formula connected with deriving equations for both vertical and horizontal parabolas? Eplore Deriving the Standard-Form Equation of
More informationAlgebra 2 Unit 2 Practice
Algebra Unit Practice LESSON 7-1 1. Consider a rectangle that has a perimeter of 80 cm. a. Write a function A(l) that represents the area of the rectangle with length l.. A rectangle has a perimeter of
More informationProperties of the Graph of a Quadratic Function. has a vertex with an x-coordinate of 2 b } 2a
0.2 Graph 5 a 2 b c Before You graphed simple quadratic functions. Now You will graph general quadratic functions. Wh? So ou can investigate a cable s height, as in Eample 4. Ke Vocabular minimum value
More information3.1-Quadratic Functions & Inequalities
3.1-Quadratic Functions & Inequalities Quadratic Functions: Quadratic functions are polnomial functions of the form also be written in the form f ( ) a( h) k. f ( ) a b c. A quadratic function ma Verte
More informationReteaching (continued)
Quadratic Functions and Transformations If a, the graph is a stretch or compression of the parent function b a factor of 0 a 0. 0 0 0 0 0 a a 7 The graph is a vertical The graph is a vertical compression
More informationSection 2.5: Graphs of Functions
Section.5: Graphs of Functions Objectives Upon completion of this lesson, ou will be able to: Sketch the graph of a piecewise function containing an of the librar functions. o Polnomial functions of degree
More informationx x 5, x no real solutions. x a. 103 feet. b seconds
BRIDGE TO ALGEBRA B. 0. 9 3. 40 4. 5. 6 6. 9 5 6 7. 4 8. 3 9. 0 0. 7. 5,. 5, 3. no real solutions 4. 3 5 4 5. a. 03 feet b. 5.3 seconds 6. a. There are two times when the ball is si feet above the ground.
More informationFair Game Review. Chapter 5. Input, x Output, y. 1. Input, x Output, y. Describe the pattern of inputs x and outputs y.
Name Date Chapter Fair Game Review Describe the pattern of inputs and outputs.. Input, utput,. 8 Input, utput,. Input, 9. utput, 8 Input, utput, 9. The table shows the number of customers in hours. Describe
More informationChapter Start Thinking! For use before Activity 6.1. For use before Activity Start Thinking! For use before Lesson
. Enrichment and Etension. a =, b =. a =, b =. a =, b =. a =, b =. a =, b is an number ecept.. a =, b =. a =, b =. a =, b =. Check students work.. Puzzle PAY HIM Etension. Start Thinking! For use before
More informationLaurie s Notes. Overview of Section 3.5
Overview of Section.5 Introduction Sstems of linear equations were solved in Algebra using substitution, elimination, and graphing. These same techniques are applied to nonlinear sstems in this lesson.
More informationFinal Exam Review Part 2 #4
Final Eam Review Part # Intermediate Algebra / MAT 135 Fall 01 Master (Prof. Fleischner) Student Name/ID: 1. Solve for, where is a real number. + = 8. Solve for, where is a real number. 9 1 = 3. Solve
More informationFinal Exam Review Part 2 #4
Final Eam Review Part # Intermediate Algebra / MAT 135 Fall 01 Master (Prof. Fleischner) Student Name/ID: 1. Solve for, where is a real number. + =. Solve for, where is a real number. 9 1 = 3. Solve for,
More informationRecord and Practice Journal Answer Key
Record and Practice Journal Answer Ke Chapter Fair Game Review......... F. floors......... $. groups. Activit. Triangle. a. The sum of the angle measures of a triangle is. Answer should include, but is
More informationState whether the following statements are true or false: 27.
Cumulative MTE -9 Review This packet includes major developmental math concepts that students ma use to prepare for the VPT Math (Virginia Placement Test for Math or for students to use to review essential
More informationSkills Practice Skills Practice for Lesson 1.1
Skills Practice Skills Practice for Lesson. Name Date Lots and Projectiles Introduction to Quadratic Functions Vocabular Give an eample of each term.. quadratic function 9 0. vertical motion equation s
More informationMath 084 Spring 2014 Exam 3 (Final) Preperation Ch 4 et al v01 Dressler. Name
Math 0 Spring 01 Eam 3 (Final) Preperation Ch et al v01 Dressler Name Determine whether the ordered pair is a solution of the sstem. 1) (-3, ) + = 3 - = -9 Solve the sstem b graphing. If there is no solution
More information1. Without the use of your calculator, evaluate each of the following quadratic functions for the specified input values. (c) ( )
Name: Date: QUADRATIC FUNCTION REVIEW FLUENCY Algebra II 1. Without the use of our calculator, evaluate each of the following quadratic functions for the specified input values. (a) g( x) g g ( 5) ( 3)
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question
Midterm Review 0 Precalculu Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question ) A graph of a function g is shown below. Find g(0). (-, ) (-, 0) - -
More informationLearning Targets: Standard Form: Quadratic Function. Parabola. Vertex Max/Min. x-coordinate of vertex Axis of symmetry. y-intercept.
Name: Hour: Algebra A Lesson:.1 Graphing Quadratic Functions Learning Targets: Term Picture/Formula In your own words: Quadratic Function Standard Form: Parabola Verte Ma/Min -coordinate of verte Ais of
More informationState whether the following statements are true or false: 30. 1
Cumulative MTE -9 Review This packet includes major developmental math concepts that students ma use to prepare for the VPT Math (Virginia Placement Test for Math or for students to use to review essential
More informationSection 9.1 Video Guide Distance and Midpoint Formulas
Objectives: 1. Use the Distance Formula 2. Use the Midpoint Formula Section 9.1 Video Guide Distance and Midpoint Formulas Section 9.1 Objective 1: Use the Distance Formula Video Length 8:27 1. Eample:
More information9 (0, 3) and solve equations to earn full credit.
Math 0 Intermediate Algebra II Final Eam Review Page of Instructions: (6, ) Use our own paper for the review questions. For the final eam, show all work on the eam. (-6, ) This is an algebra class do not
More informationChapter 5 Smartboard Notes
Name Chapter 5 Smartboard Notes 10.1 Graph ax 2 + c Learning Outcome To graph simple quadratic functions Quadratic function A non linear function that can be written in the standard form y = ax 2 + bx
More information9-1. The Function with Equation y = ax 2. Vocabulary. Graphing y = x 2. Lesson
Chapter 9 Lesson 9-1 The Function with Equation = a BIG IDEA The graph of an quadratic function with equation = a, with a 0, is a parabola with verte at the origin. Vocabular parabola refl ection-smmetric
More informationFair Game Review. Chapter 9. Find the square root(s) ± Find the side length of the square. 7. Simplify Simplify 63.
Name Date Chapter 9 Find the square root(s). Fair Game Review... 9. ±. Find the side length of the square.. s. s s Area = 9 ft s Area = 0. m 7. Simplif 0. 8. Simplif. 9. Simplif 08. 0. Simplif 88. Copright
More informationReview of Essential Skills and Knowledge
Review of Essential Skills and Knowledge R Eponent Laws...50 R Epanding and Simplifing Polnomial Epressions...5 R 3 Factoring Polnomial Epressions...5 R Working with Rational Epressions...55 R 5 Slope
More informationMATH College Algebra Review for Test 2
MATH 34 - College Algebra Review for Test 2 Sections 3. and 3.2. For f (x) = x 2 + 4x + 5, give (a) the x-intercept(s), (b) the -intercept, (c) both coordinates of the vertex, and (d) the equation of the
More informationAlgebra 1 Unit 9 Quadratic Equations
Algebra 1 Unit 9 Quadratic Equations Part 1 Name: Period: Date Name of Lesson Notes Tuesda 4/4 Wednesda 4/5 Thursda 4/6 Frida 4/7 Monda 4/10 Tuesda 4/11 Wednesda 4/12 Thursda 4/13 Frida 4/14 Da 1- Quadratic
More information20.2 Connecting Intercepts and Linear Factors
Name Class Date 20.2 Connecting Intercepts and Linear Factors Essential Question: How are -intercepts of a quadratic function and its linear factors related? Resource Locker Eplore Connecting Factors and
More informationFirst Semester Final Review NON-Graphing Calculator
Algebra First Semester Final Review NON-Graphing Calculator Name:. 1. Find the slope of the line passing through the points ( 5, ) and ( 3, 7).. Find the slope-intercept equation of the line passing through
More informationChapter 1 Graph of Functions
Graph of Functions Chapter Graph of Functions. Rectangular Coordinate Sstem and Plotting points The Coordinate Plane Quadrant II Quadrant I (0,0) Quadrant III Quadrant IV Figure. The aes divide the plane
More information3.1 Graph Quadratic Functions
3. Graph Quadratic Functions in Standard Form Georgia Performance Standard(s) MMA3b, MMA3c Goal p Use intervals of increase and decrease to understand average rates of change of quadratic functions. Your
More informationVertex form of a quadratic equation
Verte form of a quadratic equation Nikos Apostolakis Spring 017 Recall 1. Last time we looked at the graphs of quadratic equations in two variables. The upshot was that the graph of the equation: k = a(
More information3. TRANSLATED PARABOLAS
3. TRANSLATED PARABOLAS The Parabola with Verte V(h, k) and Aes Parallel to the ais Consider the concave up parabola with verte V(h, k) shown below. This parabola is obtained b translating the parabola
More informationSummer Math Packet (revised 2017)
Summer Math Packet (revised 07) In preparation for Honors Math III, we have prepared a packet of concepts that students should know how to do as these concepts have been taught in previous math classes.
More informationMATH 91 Final Study Package Name
MATH 91 Final Stud Package Name Solve the sstem b the substitution method. If there is no solution or an infinite number of solutions, so state. Use set notation to epress the solution set. 1) - = 1 1)
More informationVertex Form of a Parabola
Verte Form of a Parabola In this investigation ou will graph different parabolas and compare them to what is known as the Basic Parabola. THE BASIC PARABOLA Equation = 2-3 -2-1 0 1 2 3 verte? What s the
More information5-4. Focus and Directrix of a Parabola. Key Concept Parabola VOCABULARY TEKS FOCUS ESSENTIAL UNDERSTANDING
5- Focus and Directri of a Parabola TEKS FOCUS VOCABULARY TEKS ()(B) Write the equation of a parabola using given attributes, including verte, focus, directri, ais of smmetr, and direction of opening.
More informationClasswork #40: Final Review: Solving Equations, Word Problems, Linear Equations, Systems of Linear Equations
Classwork #0: Final Review: Solving Equations, Word Problems, Linear Equations, Sstems of Linear Equations Solving Equations: Isolate the variable! Things to watch for: when ou have parentheses the inequalit
More informationMath 101 chapter six practice exam MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Math 1 chapter si practice eam MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Which equation matches the given calculator-generated graph and description?
More informationPath of the Horse s Jump y 3. transformation of the graph of the parent quadratic function, y 5 x 2.
- Quadratic Functions and Transformations Content Standards F.BF. Identif the effect on the graph of replacing f() b f() k, k f(), f(k), and f( k) for specific values of k (both positive and negative)
More informationCh 5 Alg 2 L2 Note Sheet Key Do Activity 1 on your Ch 5 Activity Sheet.
Ch Alg L Note Sheet Ke Do Activit 1 on our Ch Activit Sheet. Chapter : Quadratic Equations and Functions.1 Modeling Data With Quadratic Functions You had three forms for linear equations, ou will have
More informationAdvanced Algebra 2 Final Review Packet KG Page 1 of Find the slope of the line passing through (3, -1) and (6, 4).
Advanced Algebra Final Review Packet KG 0 Page of 8. Evaluate (7 ) 0 when and. 7 7. Solve the equation.. Solve the equation.. Solve the equation. 6. An awards dinner costs $ plus $ for each person making
More informationLinear Equation Theory - 2
Algebra Module A46 Linear Equation Theor - Copright This publication The Northern Alberta Institute of Technolog 00. All Rights Reserved. LAST REVISED June., 009 Linear Equation Theor - Statement of Prerequisite
More information206 Calculus and Structures
06 Calculus and Structures CHAPTER 4 CURVE SKETCHING AND MAX-MIN II Calculus and Structures 07 Copright Chapter 4 CURVE SKETCHING AND MAX-MIN II 4. INTRODUCTION In Chapter, we developed a procedure for
More informationGraphing Calculator Computations 2
Graphing Calculator Computations A) Write the graphing calculator notation and B) Evaluate each epression. 4 1) 15 43 8 e) 15 - -4 * 3^ + 8 ^ 4/ - 1) ) 5 ) 8 3 3) 3 4 1 8 3) 7 9 4) 1 3 5 4) 5) 5 5) 6)
More information