REVIEW FOR THE FIRST SEMESTER EXAM
|
|
- Theodore Washington
- 5 years ago
- Views:
Transcription
1 Algebra II Name Period Date REVIEW FOR THE FIRST SEMESTER EXAM You must NEATLY show ALL of your work ON SEPARATE PAPER in order to receive full credit! All graphs must be done on GRAPH PAPER! This review is due on exam day. Chapter 1 1. Find the next two numbers in each pattern. a. 5,, 1,, b. 144, 7, 6,,. Name all subsets of real numbers to which each number belongs: a. 5 b. 5 c. 5 d. 5. Name the property that is illustrated in each example. 5 4 a b. 1 1 c. 1 d. 4 4 x 4 x Write an inequality that represents the sentence, the difference of a number and is at least Evaluate a a for a 6. Solve: 8w The expression 0 6h models the cost in dollars of renting scuba gear from the water sports store. In the expression, h represents the number of hours the scuba gear is rented for. What is the cost of renting scuba gear for 4 hours? Include units in your answer! 8. Solve the equation for x. x 6 10a 9. Solve each inequality and graph the solution(s) on a number line. 1 a. c 6c 7 b. 8 x 1 and x 10. Solve the equation and graph the solution(s) on a number line. x Solve the inequality and graph the solution(s) on a number line. x Solve x 5 4x 9. Check for extraneous solutions. 1. Determine whether each equation is always, sometimes, or never true. 1 m 6 m 6 b. d 5 6 a. 14. Avin and Anuj are identical twins. Their brother Rohan is five years older than the twins. The sum of the three brothers ages is 5. Write a single equation to determine how old Avin and Anuj are, then determine their ages.
2 Chapter 1. Find the domain and range of each relation. Then determine if the relation is a function. a. {(, 5), (, ), ( 5,0), (4, )} b. c.. Evaluate the function f x x 6 for x Write an equation in slope-intercept form for the line shown in the graph at right. 4. For x 10 y : a. Write the equation in slope-intercept form. b. Find the slope and y-intercept of the line. Write the y-intercept as an ordered pair Graph y x Find the x- and y-intercepts of x y 1. Then graph the equation. 7. Write the point-slope form equation of the line that passes through 4, and 6,1 8. Write 4 5 y x in standard form with integer coefficients. 9. Write an equation of a line that has a slope that is undefined. 10. Write an equation of a line that has a slope that is zero. 11. Write the slope-intercept form of the line that passes through (4, 1) and is perpendicular to 1 y x Write the slope-intercept form of the line that passes through, x 4y 16. and is parallel to 1. Describe the transformation from the parent function f x for f x 8 y. 14. Write the equation of the transformed graph for the parent function f x x that has been shifted right, reflected over the x-axis, and vertically stretched by a factor of. 15. The graph of f x is shown on the grid below and a table of values of the key points of f x has been provided. Identify the values of h, and k. Apply the transformations to the table, then use the points from the new table to sketch the transformed graph. Key points of f x: x y y f x a = h = k = x + h ay + k
3 16. Describe each transformation from the parent function. a. y x 4 b. y x Evaluate the piecewise function x 6 if x f for the given value. x 4 if x a. f 4= b. f = c. f 18. Graph the piecewise function. m x x x 1 if if x 1 x 1 Chapter 1. Classify the system of two equations as independent, dependent, or inconsistent. a. The system has no solutions. b. A system has exactly one solution. c. The system has infinitely many solutions. d. The graph of the system is two lines that intersect at one point. e. The graph of the system is two parallel lines. f. The graph of the system is one line.. Solve each system of equations. a. x y 14 x y 6-9x + y 6. Solve the system of equations by graphing. x + y > -1 x y 4 4. Solve the system of equations by substitution. y 4x 9 4x 5y 1 5. Solve the system of equations by elimination. x y x y z 8 6. Solve the system of equations. x y z 5 5x y z 6 b. y x y x Chapter 4 1. Write a quadratic equation in vertex form that opens down, has a vertex of (4, -5), and which has been vertically compressed by a factor of What is the y-intercept of the function y x 1 5?. What is the equation of the axis of symmetry of the function 1 y x 5 x? 4. What is the domain and range of the function y 0.5x 8? 5. What is the vertex form of y x 4x? 6. What are the solutions of x 1x 11 0?
4 7. Find the minimum/maximum value of each function. State whether it is a minimum or maximum. a. y x 5 1 b. y = x Write the equation of the parabola in vertex form whose graph has a vertex at, 5 passes through the point 0, Solve x x 0 using a graphing calculator Factor each expression completely. a. m m b. 5k 70k Solve each equation by factoring. a. x 4x 1 b. x 5x 0 1. Use the function x 5 y to find the following: a. vertex b. axis of symmetry c. opens up or down? d. max/min and its value e. y-intercept f. domain g. range h. describe the transformation(s) from the parent function 1. Find the sum. 4i 7i 14. Find the difference. 9 i 6i 15. Find each product. a. 6i 5i b. 4 8i i 4 7i Simplify each expression. a. b. i 1 i 17. Find the absolute value of the complex number: 8 5i 18. Factor over the imaginary numbers. 9x Find the value of the discriminant of x x What value of the discriminant will indicate that a quadratic equations has a. imaginary solutions b. 1 real solution c. real solutions and You may use imaginary numbers for problems 1,, and. 1. Solve each equation by finding square roots. a. x 8 0 b. 4x Solve by completing the square. a. x 6x 1 0 b. x 8x 6. Solve by using the quadratic formula. a. x 4x 6 b. 4x x 0
5 Chapter For the function y x 6x x 1 : a. Identify the degree and leading coefficient. b. Determine the end behavior. c. Determine the maximum number of turning points the graph could have.. For the graph given at the right a. Describe the end behavior. b. Determine whether the degree is even or odd. c. Determine whether the leading coefficient is positive or negative. d. Give the least possible degree of the polynomial.. Write a cubic function in standard form with zeros 1, 4, and. 4. Write a quartic function in standard form whose only real zeros are 1 and -5 and has an imaginary zero of i. 5. For the function y xx x : a. Find the zeros of each function. b. State the multiplicity of each zero. c. Sketch the graph using the zeros, y-intercept, and end behavior. 6. Find all solutions, Real and imaginary, by factoring. x x = 0 7. Find all solutions by factoring. 7x 64 = 0 SETS and MATRICES 1. Given U = {0, 1,,, 4, 5,, 0}, A = {0, 1,,, 4, 5, 6, 7, 8, 9, 10} and B = {0,, 4, 6, 8, 10, 1, 14, 16, 18, 0}, find a) A B b) A B c) A. Given A = -1-7 and B = , find a. A + B b. AB c. the determinant of B d. A -1
6
Final Exam Review Algebra Semester 1
Final Exam Review Algebra 015-016 Semester 1 Name: Module 1 Find the inverse of each function. 1. f x 10 4x. g x 15x 10 Use compositions to check if the two functions are inverses. 3. s x 7 x and t(x)
More information12/11/2018 Algebra II - Semester 1 Review
Name: Semester Review - Study Guide Score: 72 / 73 points (99%) Algebra II - Semester 1 Review Multiple Choice Identify the choice that best completes the statement or answers the question. Name the property
More information1. Answer: x or x. Explanation Set up the two equations, then solve each equation. x. Check
Thinkwell s Placement Test 5 Answer Key If you answered 7 or more Test 5 questions correctly, we recommend Thinkwell's Algebra. If you answered fewer than 7 Test 5 questions correctly, we recommend Thinkwell's
More informationNO CALCULATOR ON ANYTHING EXCEPT WHERE NOTED
Algebra II (Wilsen) Midterm Review NO CALCULATOR ON ANYTHING EXCEPT WHERE NOTED Remember: Though the problems in this packet are a good representation of many of the topics that will be on the exam, this
More informationHonors Algebra 2 Function Transformations Discovery
Honors Algebra Function Transformations Discovery Name: Date: Parent Polynomial Graphs Using an input-output table, make a rough sketch and compare the graphs of the following functions. f x x. f x x.
More informationALGEBRA 2 W/ TRIGONOMETRY MIDTERM REVIEW
Name: Block: ALGEBRA W/ TRIGONOMETRY MIDTERM REVIEW Algebra 1 Review Find Slope and Rate of Change Graph Equations of Lines Write Equations of Lines Absolute Value Functions Transformations Piecewise Functions
More informationCourse Number 432/433 Title Algebra II (A & B) H Grade # of Days 120
Whitman-Hanson Regional High School provides all students with a high- quality education in order to develop reflective, concerned citizens and contributing members of the global community. Course Number
More informationObtaining Information from a Function s Graph.
Obtaining Information from a Function s Graph Summary about using closed dots, open dots, and arrows on the graphs 1 A closed dot indicate that the graph does not extend beyond this point and the point
More informationAlgebra 1 Semester 2 Final Review
Team Awesome 011 Name: Date: Period: Algebra 1 Semester Final Review 1. Given y mx b what does m represent? What does b represent?. What axis is generally used for x?. What axis is generally used for y?
More informationQuadratic Equations. Learning Objectives. Quadratic Function 2. where a, b, and c are real numbers and a 0
Quadratic Equations Learning Objectives 1. Graph a quadratic function using transformations. Identify the vertex and axis of symmetry of a quadratic function 3. Graph a quadratic function using its vertex,
More informationExam 2 Review. 2. What the difference is between an equation and an expression?
Exam 2 Review Chapter 1 Section1 Do You Know: 1. What does it mean to solve an equation? 2. What the difference is between an equation and an expression? 3. How to tell if an equation is linear? 4. How
More information3, 10,( 2, 4) Name. CP Algebra II Midterm Review Packet Unit 1: Linear Equations and Inequalities. Solve each equation. 3.
Name CP Algebra II Midterm Review Packet 018-019 Unit 1: Linear Equations and Inequalities Solve each equation. 1. x. x 4( x 5) 6x. 8x 5(x 1) 5 4. ( k ) k 4 5. x 4 x 6 6. V lhw for h 7. x y b for x z Find
More information1. How many white tiles will be in Design 5 of the pattern? Explain your reasoning.
Algebra 2 Semester 1 Review Answer the question for each pattern. 1. How many white tiles will be in Design 5 of the pattern Explain your reasoning. 2. What is another way to represent the expression 3.
More informationTransformations with Quadratic Functions KEY
Algebra Unit: 05 Lesson: 0 TRY THIS! Use a calculator to generate a table of values for the function y = ( x 3) + 4 y = ( x 3) x + y 4 Next, simplify the function by squaring, distributing, and collecting
More informationFunction Transformations and Symmetry
CHAPTER Function Transformations and Symmetry The first well-documented postal system was in ancient Rome, where mail was carried by horsedrawn carriages and ox-drawn wagons. The US Postal Service delivers
More informationUNIT 3 EXPRESSIONS AND EQUATIONS Lesson 3: Creating Quadratic Equations in Two or More Variables
Guided Practice Example 1 Find the y-intercept and vertex of the function f(x) = 2x 2 + x + 3. Determine whether the vertex is a minimum or maximum point on the graph. 1. Determine the y-intercept. The
More informationUnit 1 Quadratic Functions
Unit 1 Quadratic Functions This unit extends the study of quadratic functions to include in-depth analysis of general quadratic functions in both the standard form f ( x) = ax + bx + c and in the vertex
More information+ bx + c = 0, you can solve for x by using The Quadratic Formula. x
Math 33B Intermediate Algebra Fall 01 Name Study Guide for Exam 4 The exam will be on Friday, November 9 th. You are allowed to use one 3" by 5" index card on the exam as well as a scientific calculator.
More information2/22/ Transformations but first 1.3 Recap. Section Objectives: Students will know how to analyze graphs of functions.
1 2 3 4 1.4 Transformations but first 1.3 Recap Section Objectives: Students will know how to analyze graphs of functions. 5 Recap of Important information 1.2 Functions and their Graphs Vertical line
More informationSection 6.2: Properties of Graphs of Quadratic Functions. Vertex:
Section 6.2: Properties of Graphs of Quadratic Functions determine the vertex of a quadratic in standard form sketch the graph determine the y intercept, x intercept(s), the equation of the axis of symmetry,
More informationQuadratic Functions. *These are all examples of polynomial functions.
Look at: f(x) = 4x-7 f(x) = 3 f(x) = x 2 + 4 Quadratic Functions *These are all examples of polynomial functions. Definition: Let n be a nonnegative integer and let a n, a n 1,..., a 2, a 1, a 0 be real
More informationAmphitheater School District End Of Year Algebra II Performance Assessment Review
Amphitheater School District End Of Year Algebra II Performance Assessment Review This packet is intended to support student preparation and review for the Algebra II course concepts for the district common
More information3.1 INTRODUCTION TO THE FAMILY OF QUADRATIC FUNCTIONS
3.1 INTRODUCTION TO THE FAMILY OF QUADRATIC FUNCTIONS Finding the Zeros of a Quadratic Function Examples 1 and and more Find the zeros of f(x) = x x 6. Solution by Factoring f(x) = x x 6 = (x 3)(x + )
More informationPre-Calculus 11: Final Review
Pre-Calculus 11 Name: Block: FORMULAS Sequences and Series Pre-Calculus 11: Final Review Arithmetic: = + 1 = + or = 2 + 1 Geometric: = = or = Infinite geometric: = Trigonometry sin= cos= tan= Sine Law:
More informationAlgebra II Honors Combined Study Guides Units 1-4 Unit 1 Study Guide Linear Review, 3-1, 3-2 & 4-5
Algebra II Honors Combined Study Guides Units 1-4 Unit 1 Study Guide Linear Review, 3-1, 3- & 4-5 Linear Review Be able to identify the domain, range, and inverse of a function Be able to create a relation,
More informationLesson #6: Basic Transformations with the Absolute Value Function
Lesson #6: Basic Transformations with the Absolute Value Function Recall: Piecewise Functions Graph:,, What parent function did this piecewise function create? The Absolute Value Function Algebra II with
More informationPractice Test (page 391) 1. For each line, count squares on the grid to determine the rise and the run. Use slope = rise
Practice Test (page 91) 1. For each line, count squares on the grid to determine the rise and the. Use slope = rise 4 Slope of AB =, or 6 Slope of CD = 6 9, or Slope of EF = 6, or 4 Slope of GH = 6 4,
More informationUNIT 8: SOLVING AND GRAPHING QUADRATICS. 8-1 Factoring to Solve Quadratic Equations. Solve each equation:
UNIT 8: SOLVING AND GRAPHING QUADRATICS 8-1 Factoring to Solve Quadratic Equations Zero Product Property For all numbers a & b Solve each equation: If: ab 0, 1. (x + 3)(x 5) = 0 Then one of these is true:
More informationAlgebra II Quadratic Functions
1 Algebra II Quadratic Functions 2014-10-14 www.njctl.org 2 Ta b le o f C o n te n t Key Terms click on the topic to go to that section Explain Characteristics of Quadratic Functions Combining Transformations
More informationUNIT 1: NUMBER LINES, INTERVALS, AND SETS
ALGEBRA II CURRICULUM OUTLINE 2011-2012 OVERVIEW: 1. Numbers, Lines, Intervals and Sets 2. Algebraic Manipulation: Rational Expressions and Exponents 3. Radicals and Radical Equations 4. Function Basics
More informationUnit #3: Quadratic Functions Lesson #13: The Almighty Parabola. Day #1
Algebra I Unit #3: Quadratic Functions Lesson #13: The Almighty Parabola Name Period Date Day #1 There are some important features about the graphs of quadratic functions we are going to explore over the
More information0,0 is referred to as the end point.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Chapter 2: Radical Functions 2.1 Radical Functions and Transformations (Day 1) For the function y x, the radicand, x, must
More informationAlgebra 2CP S1 Final Exam Information. Your final exam will consist of two parts: Free Response and Multiple Choice
Algebra 2CP Name Algebra 2CP S1 Final Exam Information Your final exam will consist of two parts: Free Response and Multiple Choice Part I: Free Response: Five questions, 10 points each (50 points total),
More informationSection 18-1: Graphical Representation of Linear Equations and Functions
Section 18-1: Graphical Representation of Linear Equations and Functions Prepare a table of solutions and locate the solutions on a coordinate system: f(x) = 2x 5 Learning Outcome 2 Write x + 3 = 5 as
More informationLinear Functions. College Algebra
Linear Functions College Algebra Linear Function A linear function is a function whose graph is a straight line. Linear functions can be written in the slope-intercept form of a line: f(x) = mx + b where
More informationMAC Learning Objectives. Transformation of Graphs. Module 5 Transformation of Graphs. - A Library of Functions - Transformation of Graphs
MAC 1105 Module 5 Transformation of Graphs Learning Objectives Upon completing this module, you should be able to: 1. Recognize the characteristics common to families of functions. 2. Evaluate and graph
More informationMAC Module 5 Transformation of Graphs. Rev.S08
MAC 1105 Module 5 Transformation of Graphs Learning Objectives Upon completing this module, you should be able to: 1. Recognize the characteristics common to families of functions. 2. Evaluate and graph
More informationPOLYNOMIALS Graphing Polynomial Functions Common Core Standard
K Polynomials, Lesson 6, Graphing Polynomial Functions (r. 2018) POLYNOMIALS Graphing Polynomial Functions Common Core Standard Next Generation Standard F-BF.3 Identify the effect on the graph of replacing
More informationMAC 1105 Fall Term 2018
MAC 1105 Fall Term 2018 Each objective covered in MAC 1105 is listed below. Along with each objective is the homework list used with MyMathLab (MML) and a list to use with the text (if you want to use
More informationPolynomial and Rational Functions. Copyright Cengage Learning. All rights reserved.
2 Polynomial and Rational Functions Copyright Cengage Learning. All rights reserved. 2.1 Quadratic Functions Copyright Cengage Learning. All rights reserved. What You Should Learn Analyze graphs of quadratic
More informationCourse of study- Algebra Introduction: Algebra 1-2 is a course offered in the Mathematics Department. The course will be primarily taken by
Course of study- Algebra 1-2 1. Introduction: Algebra 1-2 is a course offered in the Mathematics Department. The course will be primarily taken by students in Grades 9 and 10, but since all students must
More informationRadical Functions. Attendance Problems. Identify the domain and range of each function.
Page 1 of 12 Radical Functions Attendance Problems. Identify the domain and range of each function. 1. f ( x) = x 2 + 2 2. f ( x) = 3x 3 Use the description to write the quadratic function g based on the
More informationALGEBRA II A CURRICULUM OUTLINE
ALGEBRA II A CURRICULUM OUTLINE 2013-2014 OVERVIEW: 1. Linear Equations and Inequalities 2. Polynomial Expressions and Equations 3. Rational Expressions and Equations 4. Radical Expressions and Equations
More information4.3 Quadratic functions and their properties
4.3 Quadratic functions and their properties A quadratic function is a function defined as f(x) = ax + x + c, a 0 Domain: the set of all real numers x-intercepts: Solutions of ax + x + c = 0 y-intercept:
More informationWK # Given: f(x) = ax2 + bx + c
Alg2H Chapter 5 Review 1. Given: f(x) = ax2 + bx + c Date or y = ax2 + bx + c Related Formulas: y-intercept: ( 0, ) Equation of Axis of Symmetry: x = Vertex: (x,y) = (, ) Discriminant = x-intercepts: When
More informationWarm Up. Factor the following numbers and expressions. Multiply the following factors using either FOIL or Box Method
Warm Up Factor the following numbers and expressions 1. 36 2. 36x 3 + 48x 2 + 24x Multiply the following factors using either FOIL or Box Method 3. (3x 2)(x 1) 4. (x 2)(x + 3) Objectives Recognize standard
More informationThe x-intercept can be found by setting y = 0 and solving for x: 16 3, 0
y=-3/4x+4 and y=2 x I need to graph the functions so I can clearly describe the graphs Specifically mention any key points on the graphs, including intercepts, vertex, or start/end points. What is the
More informationThings to Know for the Algebra I Regents
Types of Numbers: Real Number: any number you can think of (integers, rational, irrational) Imaginary Number: square root of a negative number Integers: whole numbers (positive, negative, zero) Things
More informationHonors Precalculus: Solving equations and inequalities graphically and algebraically. Page 1
Solving equations and inequalities graphically and algebraically 1. Plot points on the Cartesian coordinate plane. P.1 2. Represent data graphically using scatter plots, bar graphs, & line graphs. P.1
More informationMathematics Scope & Sequence Algebra I
Mathematics Scope & Sequence 2016-17 Algebra I Revised: June 20, 2016 First Grading Period (24 ) Readiness Standard(s) Solving Equations and Inequalities A.5A solve linear equations in one variable, including
More informationAlgebra 2 Semester 1 (#2221)
Instructional Materials for WCSD Math Common Finals The Instructional Materials are for student and teacher use and are aligned to the 2016-2017 Course Guides for the following course: Algebra 2 Semester
More information2.4. A LIBRARY OF PARENT FUNCTIONS
2.4. A LIBRARY OF PARENT FUNCTIONS 1 What You Should Learn Identify and graph linear and squaring functions. Identify and graph cubic, square root, and reciprocal function. Identify and graph step and
More informationQUADRATIC FUNCTIONS: MINIMUM/MAXIMUM POINTS, USE OF SYMMETRY. 7.1 Minimum/Maximum, Recall: Completing the square
CHAPTER 7 QUADRATIC FUNCTIONS: MINIMUM/MAXIMUM POINTS, USE OF SYMMETRY 7.1 Minimum/Maximum, Recall: Completing the square The completing the square method uses the formula x + y) = x + xy + y and forces
More informationSection 4.1 Review of Quadratic Functions and Graphs (3 Days)
Integrated Math 3 Name What can you remember before Chapter 4? Section 4.1 Review of Quadratic Functions and Graphs (3 Days) I can determine the vertex of a parabola and generate its graph given a quadratic
More informationAlgebra 2 Semester 2 Final Exam Study Outline Semester 2 Final Exam Study Tips and Information
Algebra 2 Semester 2 Final Exam Study Outline 2013 Semester 2 Final Exam Study Tips and Information The final exam is CUMULATIVE and will include all concepts taught from Chapter 1 through Chapter 13.
More informationMath Analysis Chapter 1 Notes: Functions and Graphs
Math Analysis Chapter 1 Notes: Functions and Graphs Day 6: Section 1-1 Graphs Points and Ordered Pairs The Rectangular Coordinate System (aka: The Cartesian coordinate system) Practice: Label each on the
More informationSolving Simple Quadratics 1.0 Topic: Solving Quadratics
Ns Solving Simple Quadratics 1.0 Topic: Solving Quadratics Date: Objectives: SWBAT (Solving Simple Quadratics and Application dealing with Quadratics) Main Ideas: Assignment: Square Root Property If x
More informationChapter 3 Practice Test
1. Complete parts a c for each quadratic function. a. Find the y-intercept, the equation of the axis of symmetry, and the x-coordinate of the vertex. b. Make a table of values that includes the vertex.
More informationAlgebra II: Strand 3. Quadratic Functions; Topic 2. Digging Deeper; Task 3.2.1
1 TASK 3..1: PUTTING IT TOGETHER Solutions 1. Each of the following quadratic functions is given in standard form ( y = ax + bx + c ). For each function: Transform the function to the form y = a(x h) +
More informationYou should be able to plot points on the coordinate axis. You should know that the the midpoint of the line segment joining (x, y 1 1
Name GRAPHICAL REPRESENTATION OF DATA: You should be able to plot points on the coordinate axis. You should know that the the midpoint of the line segment joining (x, y 1 1 ) and (x, y ) is x1 x y1 y,.
More informationMath 125 Little Book Homework Chapters 7, 10, 11, and 12
Math 125 Little Book Homework Chapters 7, 10, 11, and 12 Do NOT copy the book follow the guidelines given for each section. NO CREDIT will be given if you copy the book! You earn 2 points if you turn in
More informationReteaching Transforming Linear Functions
Name Date Class Transforming Linear Functions INV 6 You have graphed linear functions on the coordinate plane. Now you will investigate transformations of the parent function for a linear function, f(x)
More informationToday is the last day to register for CU Succeed account AND claim your account. Tuesday is the last day to register for my class
Today is the last day to register for CU Succeed account AND claim your account. Tuesday is the last day to register for my class Back board says your name if you are on my roster. I need parent financial
More informationTest 3 review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Test 3 review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Approximate the coordinates of each turning point by graphing f(x) in the standard viewing
More informationMath Analysis Chapter 1 Notes: Functions and Graphs
Math Analysis Chapter 1 Notes: Functions and Graphs Day 6: Section 1-1 Graphs; Section 1- Basics of Functions and Their Graphs Points and Ordered Pairs The Rectangular Coordinate System (aka: The Cartesian
More informationEnd Behavior and Symmetry
Algebra 2 Interval Notation Name: Date: Block: X Characteristics of Polynomial Functions Lesson Opener: Graph the function using transformations then identify key characteristics listed below. 1. y x 2
More informationMAC Rev.S Learning Objectives. Learning Objectives (Cont.) Module 4 Quadratic Functions and Equations
MAC 1140 Module 4 Quadratic Functions and Equations Learning Objectives Upon completing this module, you should be able to 1. understand basic concepts about quadratic functions and their graphs.. complete
More informationModule 1. Name: Date: Period: Find the following function values. 4. Find the following: Domain. Range. The graph is increasing over the interval
Name: Date: Period: Algebra Fall Final Exam Review My Exam Date Is : Module 1 Find the following function values. f(x) = 3x + g(x) = x h(x) = x 3 1. g(f(x)). h(3) g(3) 3. g(f()) 4. Find the following:
More informationStart Fred Functions. Quadratic&Absolute Value Transformations. Graphing Piecewise Functions Intro. Graphing Piecewise Practice & Review
Honors CCM2 Unit 6 Name: Graphing Advanced Functions This unit will get into the graphs of simple rational (inverse variation), radical (square and cube root), piecewise, step, and absolute value functions.
More informationVertex maximum or minimum Axis of Symmetry OPENS: UP MINIMUM
5.1 GRAPHING QUADRATIC FUNCTIONS IN STANDARD FORM & MUTIPLYING BINOMIALS Standard Form of a Quadratic: y ax bx c or f x ax bx c ex. y x 5x 13 a= b= c=. Every function/graph in the Quadratic family originates
More informationQuadratic Functions. Chapter Properties of Quadratic Functions... p Investigating Quadratic Functions... p. 6 in Vertex Form: Part 1
Chapter 3 Quadratic Functions 3. Properties of Quadratic Functions........... p. 1 3.1 Investigating Quadratic Functions........... p. 6 in Vertex Form: Part 1 3.1 Investigating Quadratic Functions...........
More informationPre-Calculus Summer Assignment
Name: Pre-Calculus Summer Assignment Due Date: The beginning of class on September 8, 017. The purpose of this assignment is to have you practice the mathematical skills necessary to be successful in Pre-Calculus.
More informationIntegrated Algebra 2 and Trigonometry. Quarter 1
Quarter 1 I: Functions: Composition I.1 (A.42) Composition of linear functions f(g(x)). f(x) + g(x). I.2 (A.42) Composition of linear and quadratic functions II: Functions: Quadratic II.1 Parabola The
More information3x 2 + 7x + 2. A 8-6 Factor. Step 1. Step 3 Step 4. Step 2. Step 1 Step 2 Step 3 Step 4
A 8-6 Factor. Step 1 3x 2 + 7x + 2 Step 2 Step 3 Step 4 3x 2 + 7x + 2 3x 2 + 7x + 2 Step 1 Step 2 Step 3 Step 4 Factor. 1. 3x 2 + 4x +1 = 2. 3x 2 +10x + 3 = 3. 3x 2 +13x + 4 = A 8-6 Name BDFM? Why? Factor.
More informationSection 6 Quadratic Functions Part 2
Section 6 Quadratic Functions Part 2 The following Mathematics Florida Standards will be covered in this section: MAFS.912.A-CED.1.2 Create equations in two or more variables to represent relationships
More informationQUESTIONS 1 10 MAY BE DONE WITH A CALCULATOR QUESTIONS ARE TO BE DONE WITHOUT A CALCULATOR. Name
QUESTIONS 1 10 MAY BE DONE WITH A CALCULATOR QUESTIONS 11 5 ARE TO BE DONE WITHOUT A CALCULATOR Name 2 CALCULATOR MAY BE USED FOR 1-10 ONLY Use the table to find the following. x -2 2 5-0 7 2 y 12 15 18
More informationUnit 2 Day 11. Quadratic Inequalities & Systems
Unit Day 11 Quadratic Inequalities & Systems 1 Warm Up 1. Given the following functions, specifically describe the transformation from the identity function y = x a. y = (x+3) 7 b. y = 5x + 1 c. y = ½(x
More informationUnit 2: Functions and Graphs
AMHS Precalculus - Unit 16 Unit : Functions and Graphs Functions A function is a rule that assigns each element in the domain to exactly one element in the range. The domain is the set of all possible
More information1.1 - Functions, Domain, and Range
1.1 - Functions, Domain, and Range Lesson Outline Section 1: Difference between relations and functions Section 2: Use the vertical line test to check if it is a relation or a function Section 3: Domain
More informationGraphing Absolute Value Functions
Graphing Absolute Value Functions To graph an absolute value equation, make an x/y table and plot the points. Graph y = x (Parent graph) x y -2 2-1 1 0 0 1 1 2 2 Do we see a pattern? Desmos activity: 1.
More informationGraph each function. State the domain, the vertex (min/max point), the range, the x intercepts, and the axis of symmetry.
HW Worksheet Name: Graph each function. State the domain, the vertex (min/max point), the range, the x intercepts, and the axis of smmetr..) f(x)= x + - - - - x - - - - Vertex: Max or min? Axis of smmetr:.)
More informationMath 370 Exam 1 Review Name. Use the vertical line test to determine whether or not the graph is a graph in which y is a function of x.
Math 370 Exam 1 Review Name Determine whether the relation is a function. 1) {(-6, 6), (-6, -6), (1, 3), (3, -8), (8, -6)} Not a function The x-value -6 corresponds to two different y-values, so this relation
More informationAlgebra II Chapter 5
Algebra II Chapter 5 5.1 Quadratic Functions The graph of a quadratic function is a parabola, as shown at rig. Standard Form: f ( x) = ax2 + bx + c vertex: b 2a, f b 2a a < 0 graph opens down a > 0 graph
More informationKEY Algebra: Unit 10 Graphing Quadratic Equations & other Relations
Name: KEY Algebra: Unit 10 Graphing Quadratic Equations & other Relations Date: Test Bank Part I: Answer all 15 questions in this part. Each correct answer will receive credits. No partial credit will
More informationFoundations of Math II
Foundations of Math II Unit 6b: Toolkit Functions Academics High School Mathematics 6.6 Warm Up: Review Graphing Linear, Exponential, and Quadratic Functions 2 6.6 Lesson Handout: Linear, Exponential,
More informationMATHS METHODS QUADRATICS REVIEW. A reminder of some of the laws of expansion, which in reverse are a quick reference for rules of factorisation
MATHS METHODS QUADRATICS REVIEW LAWS OF EXPANSION A reminder of some of the laws of expansion, which in reverse are a quick reference for rules of factorisation a) b) c) d) e) FACTORISING Exercise 4A Q6ace,7acegi
More information3.7. Vertex and tangent
3.7. Vertex and tangent Example 1. At the right we have drawn the graph of the cubic polynomial f(x) = x 2 (3 x). Notice how the structure of the graph matches the form of the algebraic expression. The
More informationReview for Mastery Using Graphs and Tables to Solve Linear Systems
3-1 Using Graphs and Tables to Solve Linear Systems A linear system of equations is a set of two or more linear equations. To solve a linear system, find all the ordered pairs (x, y) that make both equations
More informationREVIEW, pages
REVIEW, pages 69 697 8.. Sketch a graph of each absolute function. Identif the intercepts, domain, and range. a) = ƒ - + ƒ b) = ƒ ( + )( - ) ƒ 8 ( )( ) Draw the graph of. It has -intercept.. Reflect, in
More informationWHAT YOU SHOULD LEARN
GRAPHS OF EQUATIONS WHAT YOU SHOULD LEARN Sketch graphs of equations. Find x- and y-intercepts of graphs of equations. Use symmetry to sketch graphs of equations. Find equations of and sketch graphs of
More informationVoluntary State Curriculum Algebra II
Algebra II Goal 1: Integration into Broader Knowledge The student will develop, analyze, communicate, and apply models to real-world situations using the language of mathematics and appropriate technology.
More informationCHAPTER 6 Quadratic Functions
CHAPTER 6 Quadratic Functions Math 1201: Linear Functions is the linear term 3 is the leading coefficient 4 is the constant term Math 2201: Quadratic Functions Math 3201: Cubic, Quartic, Quintic Functions
More informationUnit 5: Quadratic Functions
Unit 5: Quadratic Functions LESSON #5: THE PARABOLA GEOMETRIC DEFINITION DIRECTRIX FOCUS LATUS RECTUM Geometric Definition of a Parabola Quadratic Functions Geometrically, a parabola is the set of all
More informationChapter 2: Polynomial and Rational Functions Power Standard #7
Chapter 2: Polynomial and Rational s Power Standard #7 2.1 Quadratic s Lets glance at the finals. Learning Objective: In this lesson you learned how to sketch and analyze graphs of quadratic functions.
More informationQuadratics. March 18, Quadratics.notebook. Groups of 4:
Quadratics Groups of 4: For your equations: a) make a table of values b) plot the graph c) identify and label the: i) vertex ii) Axis of symmetry iii) x- and y-intercepts Group 1: Group 2 Group 3 1 What
More information2018 PRE-CAL PAP SUMMER REVIEW
NAME: DATE: 018 PRE-CAL PAP SUMMER REVIEW ***Due August 1 st *** Email To: Schmidtam@needvilleisd.com or Drop off & put in my box at the High School You can see this site for help: https://www.khanacademy.org/math/algebra
More informationPre-Calculus Summer Assignment
Pre-Calculus Summer Assignment Identify the vertex and the axis of symmetry of the parabola. Identify points corresponding to P and Q. 1. 2. Find a quadratic model for the set of values. 3. x 2 0 4 f(x)
More informationChapter P: Preparation for Calculus
1. Which of the following is the correct graph of y = x x 3? E) Copyright Houghton Mifflin Company. All rights reserved. 1 . Which of the following is the correct graph of y = 3x x? E) Copyright Houghton
More informationAlgebra I Notes Absolute Value Functions Unit 04c
OBJECTIVES: F.IF.B.4 Interpret functions that arise in applications in terms of the context. For a function that models a relationship between two quantities, interpret key features of graphs and tables
More informationUnit 12 Special Functions
Algebra Notes Special Functions Unit 1 Unit 1 Special Functions PREREQUISITE SKILLS: students should be able to describe a relation and a function students should be able to identify the domain and range
More information