GRAPHING QUADRATIC FUNCTIONS IN STANDARD FORM
|
|
|
- Barbra Leonard
- 5 years ago
- Views:
Transcription
1 FOM 11 T7 GRAPHING QUADRATIC FUNCTIONS IN STANDARD FORM 1 1 GRAPHING QUADRATIC FUNCTIONS IN STANDARD FORM I) THE STANDARD FORM OF A QUADRATIC FUNCTION (PARABOLA) IS = a +b +c. To graph a quadratic function in standard form ou must know where the verte is relative to the -ais. The verte ma be to the left of, on or to the right of the -ais. Recall that c indicates the location of the -intercept. We can use the signs of a and p to indicate the position of the verte relative to the -ais. Complete the investigation below to learn how to determine the position of the verte relative to the -ais of a quadratic function in standard form. II) INVESTIGATION 1: Answer the questions for each quadratic function. Answer the summar questions at the end of the investigation. 1) = State the position of the verte relative to the -ais ) = State the position of the verte relative to the -ais ) = State the position of the verte relative to the -ais R. Ashb 017. Duplication b permission onl.
2 FOM 11 T7 GRAPHING QUADRATIC FUNCTIONS IN STANDARD FORM 1 ) = + State the position of the verte relative to the -ais. 5) = + State the position of the verte relative to the -ais ) = State the position of the verte relative to the -ais R. Ashb 017. Duplication b permission onl.
3 FOM 11 T7 GRAPHING QUADRATIC FUNCTIONS IN STANDARD FORM 1 3 7) = State the position of the verte relative to the -ais ) = State the position of the verte relative to the -ais ) = State the position of the verte relative to the -ais R. Ashb 017. Duplication b permission onl.
4 FOM 11 T7 GRAPHING QUADRATIC FUNCTIONS IN STANDARD FORM 1 ) = + State the position of the verte relative to the -ais ) = + State the position of the verte relative to the -ais ) = + 3 State the position of the verte relative to the -ais R. Ashb 017. Duplication b permission onl.
5 FOM 11 T7 GRAPHING QUADRATIC FUNCTIONS IN STANDARD FORM ) = State the position of the verte relative to the -ais ) = State the position of the verte relative to the -ais Conclusions: The verte is on the -ais when b =. The verte is on the left side of the -ais when the signs of a & b are the. The verte is on the right side of the -ais when the signs of a & b are. III) Steps to Graph Quadratic Functions in Standard Form A) USE THESE STEPS TO SOLVE OPTIMIZATION PROBLEMS 1: Use the signs of a & b to determine the position of the verte relative to the -ais and the -intercept. : Create a table of ordered pairs using values of starting at = 0 for the side of the -ais that where the verte is located until the verte is located. 3: Plot the points on a grid. Use the ais of smmetr to plots corresponding points on the other side of the parabola. R. Ashb 017. Duplication b permission onl.
6 FOM 11 T7 GRAPHING QUADRATIC FUNCTIONS IN STANDARD FORM 1 B) SAMPLE PROBLEMS 1: Stud these eamples carefull. Be sure ou understand and memorize the process used to complete them. Instructions: Graph these quadratic functions. 1. = 7 1: Use the signs of a & b to determine the position of the verte relative to the -ais and the -intercept. a = & b = The verte is the -ais : Create a table of ordered pairs using values of starting at = 0 for the side of the -ais that where the verte is located until the verte is located. b =, therefore the verte is on the -ais. Use = 0, 1, & 3 to determine ordered pairs (0) 7 = 0 7 = 7 these are the coordinates of the verte 1 (1) 7 = 1 7 = 3 () 7 = 7 = 3 3 (3) 7 = 9 7 = 3: Plot the points on a grid. Use the ais of smmetr to plots corresponding points on the other side of the parabola = 1: Use the signs of a & b to determine the position of the verte relative to the -ais and the -intercept. a = & b = The verte is on the side of the -ais Continued on the net page. R. Ashb 017. Duplication b permission onl.
7 FOM 11 T7 GRAPHING QUADRATIC FUNCTIONS IN STANDARD FORM 1 7 : Create a table of ordered pairs using values of starting at = 0 for the side of the -ais that where the verte is located until the verte is located. a & b have signs, therefore the verte is on the side of the - ais. Use =, etc. to determine ordered pairs. 0 0 (0) (0) = 0 0 = (1) (1) = 1 = 3 () () = = these are the coordinates of the verte 3 3 (3) (3) = 9 1 = 3 3: Plot the points on a grid. Use the ais of smmetr to plots corresponding points on the other side of the parabola = + 1: Use the signs of a & b to determine the position of the verte relative to the -ais and the -intercept. a = & b = The verte is on the side of the -ais : Create a table of ordered pairs using values of starting at = 0 for the side of the -ais that where the verte is located until the verte is located. a & b have the signs, therefore the verte is on the side of the - ais. Use =, etc. to determine ordered pairs. + 0 (0) + (0) = 0 0 = the coordinates of the verte are 1 ( 1) + ( 1) = 1 1 = between these two coordinates 0 ( ) + ( ) = = 0 3 ( 3) + ( 3) = 9 3 = Continued on the net page. R. Ashb 017. Duplication b permission onl.
8 FOM 11 T7 GRAPHING QUADRATIC FUNCTIONS IN STANDARD FORM 1 In this case we must calculate the coordinates of the verte as illustrated here. Calculate the equation of the ais of smmetr: = 1 + = +1 = 1 = 0.5 Calculate the minimum: = + = ( 0.5) + ( 0.5) = =.5 State the coordinates of the verte: V ( 0.5,.5) 3: Plot the points on a grid. Use the ais of smmetr to plots corresponding points on the other side of the parabola C) REQUIRED PRACTICE 1: Complete these questions. 1) Draw the graphs for the quadratic functions in question 5 on page 370. ) Answer question 11 on page ) Draw the graph for the quadratic function in question a on page R. Ashb 017. Duplication b permission onl.
9 FOM 11 T7 GRAPHING QUADRATIC FUNCTIONS IN STANDARD FORM R. Ashb 017. Duplication b permission onl.
10 FOM 11 T7 GRAPHING QUADRATIC FUNCTIONS IN STANDARD FORM 1 ASSIGNMENT: PRINT THIS INFORMATION ON YOUR OWN GRID PAPER LAST then FIRST Name T7 GRAPHING QUADRATIC FUNCTIONS IN STANDARD FORM 1 Block: Show the process required to complete each problem to avoid receiving a zero grade. Neatness Counts!!! (Marks indicated in italicized brackets) REMEMBER TO USE GRID PAPER FOR ALL ASSIGNMENTS!!! Graph these quadratic functions. State the domain and range. REMEMBER TO INCLUDE ALL INORMATION DISCUSSED IN THE CLASS. 1) = +1 ) = + 3) f ( ) = R. Ashb 017. Duplication b permission onl.
MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED
FOM 11 T9 GRAPHING LINEAR EQUATIONS REVIEW - 1 MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED 1) -INTERCEPT = the point where the graph touches or crosses the -ais. It occurs when = 0. ) -INTERCEPT = the
10 Academic Date: Enter this equation into in DESMOS. Adjust your screen to show the scales like they are shown in the grid below.
Academic Date: Open: DESMOS Graphing Calculator Task : Let s Review Linear Relationships Bill Bob s dog is out for a walk. The equation to model its distance awa from the house, d metres, after t seconds
8.5 Quadratic Functions and Their Graphs
CHAPTER 8 Quadratic Equations and Functions 8. Quadratic Functions and Their Graphs S Graph Quadratic Functions of the Form f = + k. Graph Quadratic Functions of the Form f = - h. Graph Quadratic Functions
Graphing Quadratics: Vertex and Intercept Form
Algebra : UNIT Graphing Quadratics: Verte and Intercept Form Date: Welcome to our second function famil...the QUADRATIC FUNCTION! f() = (the parent function) What is different between this function and
QUADRATIC FUNCTIONS Investigating Quadratic Functions in Vertex Form
QUADRATIC FUNCTIONS Investigating Quadratic Functions in Verte Form The two forms of a quadratic function that have been eplored previousl are: Factored form: f ( ) a( r)( s) Standard form: f ( ) a b c
4.1 Graph Quadratic Functions in
4. Graph Quadratic Functions in Standard Form Goal p Graph quadratic functions. Your Notes VOCABULARY Quadratic function Parabola Verte Ais of smmetr Minimum and maimum value PARENT FUNCTION FOR QUADRATIC
3.6 Graphing Piecewise-Defined Functions and Shifting and Reflecting Graphs of Functions
76 CHAPTER Graphs and Functions Find the equation of each line. Write the equation in the form = a, = b, or = m + b. For Eercises through 7, write the equation in the form f = m + b.. Through (, 6) and
7. f(x) = 1 2 x f(x) = x f(x) = 4 x at x = 10, 8, 6, 4, 2, 0, 2, and 4.
Section 2.2 The Graph of a Function 109 2.2 Eercises Perform each of the following tasks for the functions defined b the equations in Eercises 1-8. i. Set up a table of points that satisf the given equation.
Graphing f ( x) = ax 2 + c
. Graphing f ( ) = a + c Essential Question How does the value of c affect the graph of f () = a + c? Graphing = a + c Work with a partner. Sketch the graphs of the functions in the same coordinate plane.
Graphs of quadratics functions are parabolas opening up if a > 0, and down if a < 0. Examples:
Quadratic Functions ( ) = a + b + c Graphs o quadratics unctions are parabolas opening up i a > 0, and down i a < 0. Eamples: = = + = = 0 MATH 80 Lecture B o 5 Ronald Brent 07 All rights reserved. Notes:
REVIEW, 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
It s Not Complex Just Its Solutions Are Complex!
It s Not Comple Just Its Solutions Are Comple! Solving Quadratics with Comple Solutions 15.5 Learning Goals In this lesson, ou will: Calculate comple roots of quadratic equations and comple zeros of quadratic
Unit 4 Part 1: Graphing Quadratic Functions. Day 1: Vertex Form Day 2: Intercept Form Day 3: Standard Form Day 4: Review Day 5: Quiz
Name: Block: Unit 4 Part 1: Graphing Quadratic Functions Da 1: Verte Form Da 2: Intercept Form Da 3: Standard Form Da 4: Review Da 5: Quiz 1 Quadratic Functions Da1: Introducing.. the QUADRATIC function
3.4 Reflections of Functions
3. Reflections of Functions A coordinate grid is superimposed on a cross section of the Great Pramid, so that the -ais passes through the verte of the pramid. The -ais bisects two opposite sides of the
REMARKS. 8.2 Graphs of Quadratic Functions. A Graph of y = ax 2 + bx + c, where a > 0
8. Graphs of Quadratic Functions In an earlier section, we have learned that the graph of the linear function = m + b, where the highest power of is 1, is a straight line. What would the shape of the graph
Math 1050 Lab Activity: Graphing Transformations
Math 00 Lab Activit: Graphing Transformations Name: We'll focus on quadratic functions to eplore graphing transformations. A quadratic function is a second degree polnomial function. There are two common
12.4 The Ellipse. Standard Form of an Ellipse Centered at (0, 0) (0, b) (0, -b) center
. The Ellipse The net one of our conic sections we would like to discuss is the ellipse. We will start b looking at the ellipse centered at the origin and then move it awa from the origin. Standard Form
Transformations of y = x 2
Transformations of = Parent Parabola Lesson 11-1 Learning Targets: Describe translations of the parent function f() =. Given a translation of the function f() =, write the equation of the function. SUGGESTED
Derivatives 3: The Derivative as a Function
Derivatives : The Derivative as a Function 77 Derivatives : The Derivative as a Function Model : Graph of a Function 9 8 7 6 5 g() - - - 5 6 7 8 9 0 5 6 7 8 9 0 5 - - -5-6 -7 Construct Your Understanding
Section 9.3: Functions and their Graphs
Section 9.: Functions and their Graphs Graphs provide a wa of displaing, interpreting, and analzing data in a visual format. In man problems, we will consider two variables. Therefore, we will need to
GRAPHS AND GRAPHICAL SOLUTION OF EQUATIONS
GRAPHS AND GRAPHICAL SOLUTION OF EQUATIONS 1.1 DIFFERENT TYPES AND SHAPES OF GRAPHS: A graph can be drawn to represent are equation connecting two variables. There are different tpes of equations which
Lesson 8.1 Exercises, pages
Lesson 8.1 Eercises, pages 1 9 A. Complete each table of values. a) -3 - -1 1 3 3 11 8 5-1 - -7 3 11 8 5 1 7 To complete the table for 3, take the absolute value of each value of 3. b) - -3 - -1 1 3 3
3x 4y 2. 3y 4. Math 65 Weekly Activity 1 (50 points) Name: Simplify the following expressions. Make sure to use the = symbol appropriately.
Math 65 Weekl Activit 1 (50 points) Name: Simplif the following epressions. Make sure to use the = smbol appropriatel. Due (1) (a) - 4 (b) ( - ) 4 () 8 + 5 6 () 1 5 5 Evaluate the epressions when = - and
Graphing f ( x) = ax 2
. Graphing f ( ) = a Essential Question What are some of the characteristics of the graph of a quadratic function of the form f () = a? Graphing Quadratic Functions Work with a partner. Graph each quadratic
MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED
FOM 11 T26 QUADRATIC FUNCTIONS IN VERTEX FORM - 1 1 MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED 1) STANDARD FORM OF A QUADRATIC FUNCTION = a statement where the expression of a quadratic function is written
MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED DETERMINING THE INTERSECTIONS USING THE GRAPHING CALCULATOR
FOM 11 T15 INTERSECTIONS & OPTIMIZATION PROBLEMS - 1 1 MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED 1) INTERSECTION = a set of coordinates of the point on the grid where two or more graphed lines touch
NOTES: ALGEBRA FUNCTION NOTATION
STARTER: 1. Graph f by completing the table. f, y -1 0 1 4 5 NOTES: ALGEBRA 4.1 FUNCTION NOTATION y. Graph f 4 4 f 4 4, y --5-4 - - -1 0 1 y A Brief Review of Function Notation We will be using function
Transformations of Functions. 1. Shifting, reflecting, and stretching graphs Symmetry of functions and equations
Chapter Transformations of Functions TOPICS.5.. Shifting, reflecting, and stretching graphs Smmetr of functions and equations TOPIC Horizontal Shifting/ Translation Horizontal Shifting/ Translation Shifting,
Functions. Name. Use an XY Coordinate Pegboard to graph each line. Make a table of ordered pairs for each line. y = x + 5 x y.
Lesson 1 Functions Name Use an XY Coordinate Pegboard to graph each line. Make a table of ordered pairs for each line. 1. = + = + = 2 3 = 2 3 Using an XY Coordinate Pegboard, graph the line on a coordinate
Name: Chapter 7 Review: Graphing Quadratic Functions
Name: Chapter Review: Graphing Quadratic Functions A. Intro to Graphs of Quadratic Equations: = ax + bx+ c A is a function that can be written in the form = ax + bx+ c where a, b, and c are real numbers
Using Characteristics of a Quadratic Function to Describe Its Graph. The graphs of quadratic functions can be described using key characteristics:
Chapter Summar Ke Terms standard form of a quadratic function (.1) factored form of a quadratic function (.1) verte form of a quadratic function (.1) concavit of a parabola (.1) reference points (.) transformation
9.5 Graphing Quadratics- Parabolas
Algebra G w0ka6o tkjuptnac asuoffzttwtarr]eg ]LGLXCX. q gaalxln lrxifgthftqsq Nrae_seXrcvveEdf. 9. Graphing Quadratics- Parabolas Name ID: Date Algebra Make sure each person in our group has a worksheet
1.1 Horizontal & Vertical Translations
Unit II Transformations of Functions. Horizontal & Vertical Translations Goal: Demonstrate an understanding of the effects of horizontal and vertical translations on the graphs of functions and their related
Name Date. In Exercises 1 6, graph the function. Compare the graph to the graph of ( )
Name Date 8. Practice A In Eercises 6, graph the function. Compare the graph to the graph of. g( ) =. h =.5 3. j = 3. g( ) = 3 5. k( ) = 6. n = 0.5 In Eercises 7 9, use a graphing calculator to graph the
Unit 2: Function Transformation Chapter 1
Basic Transformations Reflections Inverses Unit 2: Function Transformation Chapter 1 Section 1.1: Horizontal and Vertical Transformations A of a function alters the and an combination of the of the graph.
Example 1: Given below is the graph of the quadratic function f. Use the function and its graph to find the following: Outputs
Quadratic Functions: - functions defined by quadratic epressions (a 2 + b + c) o the degree of a quadratic function is ALWAYS 2 - the most common way to write a quadratic function (and the way we have
4.4 Absolute Value Equations. What is the absolute value of a number? Example 1 Simplify a) 6 b) 4 c) 7 3. Example 2 Solve x = 2
4.4 Absolute Value Equations What is the absolute value of a number? Eample Simplif a) 6 b) 4 c) 7 3 Eample Solve = Steps for solving an absolute value equation: ) Get the absolute value b itself on one
Lesson 3: Investigating the Parts of a Parabola
Opening Exercise 1. Use the graph at the right to fill in the Answer column of the chart below. (You ll fill in the last column in Exercise 9.) Question Answer Bring in the Math! A. What is the shape of
Precalculus, IB Precalculus and Honors Precalculus
NORTHEAST CONSORTIUM Precalculus, IB Precalculus and Honors Precalculus Summer Pre-View Packet DUE THE FIRST DAY OF SCHOOL The problems in this packet are designed to help ou review topics from previous
9.8 Graphing Rational Functions
9. Graphing Rational Functions Lets begin with a deinition. Deinition: Rational Function A rational unction is a unction o the orm P where P and Q are polynomials. Q An eample o a simple rational unction
Answers Investigation 4
Answers Investigation Applications. a. At seconds, the flare will have traveled to a maimum height of 00 ft. b. The flare will hit the water when the height is 0 ft, which will occur at 0 seconds. c. In
This is called the vertex form of the quadratic equation. To graph the equation
Name Period Date: Topic: 7-5 Graphing ( ) Essential Question: What is the vertex of a parabola, and what is its axis of symmetry? Standard: F-IF.7a Objective: Graph linear and quadratic functions and show
3-2. Families of Graphs. Look Back. OBJECTIVES Identify transformations of simple graphs. Sketch graphs of related functions.
3-2 BJECTIVES Identif transformations of simple graphs. Sketch graphs of related functions. Families of Graphs ENTERTAINMENT At some circuses, a human cannonball is shot out of a special cannon. In order
Graphing Review. Math Tutorial Lab Special Topic
Graphing Review Math Tutorial Lab Special Topic Common Functions and Their Graphs Linear Functions A function f defined b a linear equation of the form = f() = m + b, where m and b are constants, is called
Graphing f ( x) = ax 2 + bx + c
8.3 Graphing f ( ) = a + b + c Essential Question How can ou find the verte of the graph of f () = a + b + c? Comparing -Intercepts with the Verte Work with a partner. a. Sketch the graphs of = 8 and =
Algebra 1. 7 th Standard Complete Graphs. Categories Quadratic (p. 3-9) Exponential (p ) Absolute Value (p ) Linear (p.
Algebra 1 7 th Standard Complete Graphs Categories Quadratic (p. -9) Eponential (p. 10-1) Absolute Value (p. 14-17) Linear (p. 18-9) Summative Assessment Date: Wednesda, November 8 th Page 1 Standard:
Investigating Transformations With DESMOS
MPM D0 Date: Investigating Transformations With DESMOS INVESTIGATION Part A: What if we add a constant to the x in y = x? 1. Use DESMOS to graph the following quadratic functions on the same grid. Graph
Week 10. Topic 1 Polynomial Functions
Week 10 Topic 1 Polnomial Functions 1 Week 10 Topic 1 Polnomial Functions Reading Polnomial functions result from adding power functions 1 together. Their graphs can be ver complicated, so the come up
10.2: Parabolas. Chapter 10: Conic Sections. Conic sections are plane figures formed by the intersection of a double-napped cone and a plane.
Conic sections are plane figures formed b the intersection of a double-napped cone and a plane. Chapter 10: Conic Sections Ellipse Hperbola The conic sections ma be defined as the sets of points in the
Essential Question: What are the ways you can transform the graph of the function f(x)? Resource Locker. Investigating Translations
Name Class Date 1.3 Transformations of Function Graphs Essential Question: What are the was ou can transform the graph of the function f()? Resource Locker Eplore 1 Investigating Translations of Function
Functions: The domain and range
Mathematics Learning Centre Functions: The domain and range Jackie Nicholas Jacquie Hargreaves Janet Hunter c 6 Universit of Sdne Mathematics Learning Centre, Universit of Sdne Functions In these notes
Section 4.2 Graphing Lines
Section. Graphing Lines Objectives In this section, ou will learn to: To successfull complete this section, ou need to understand: Identif collinear points. The order of operations (1.) Graph the line
Appendix A.6 Functions
A. Functions 539 RELATIONS: DOMAIN AND RANGE Appendi A. Functions A relation is a set of ordered pairs. A relation can be a simple set of just a few ordered pairs, such as {(0, ), (1, 3), (, )}, or it
Graphing Equations. The Rectangular Coordinate System
3.1 Graphing Equations The Rectangular Coordinate Sstem Ordered pair two numbers associated with a point on a graph. The first number gives the horizontal location of the point. The second gives the vertical
Intermediate Algebra. Gregg Waterman Oregon Institute of Technology
Intermediate Algebra Gregg Waterman Oregon Institute of Technolog c 2017 Gregg Waterman This work is licensed under the Creative Commons Attribution 4.0 International license. The essence of the license
Lesson 5.3 Exercises, pages
Lesson 5.3 Eercises, pages 37 3 A. Determine whether each ordered pair is a solution of the quadratic inequalit: 3 - a) (-3, ) b) (, 5) Substitute each ordered pair in» 3. L.S. ; R.S.: 3( 3) 3 L.S. 5;
Transformations of Absolute Value Functions. Compression A compression is a. function a function of the form f(x) = a 0 x - h 0 + k
- Transformations of Absolute Value Functions TEKS FOCUS VOCABULARY Compression A compression is a TEKS (6)(C) Analze the effect on the graphs of f() = when f() is replaced b af(), f(b), f( - c), and f()
5.2. Exploring Quotients of Polynomial Functions. EXPLORE the Math. Each row shows the graphs of two polynomial functions.
YOU WILL NEED graph paper coloured pencils or pens graphing calculator or graphing software Eploring Quotients of Polnomial Functions EXPLORE the Math Each row shows the graphs of two polnomial functions.
Concept: Slope of a Line
Concept: Slope of a Line Warm Up Name: The following suggested activities would serve as a review to consolidate previous learning. While promoting rich mathematical dialog, the will also provide students
Name: Thus, y-intercept is (0,40) (d) y-intercept: Set x = 0: Cover the x term with your finger: 2x + 6y = 240 Solve that equation: 6y = 24 y = 4
Name: GRAPHING LINEAR INEQUALITIES IN TWO VARIABLES SHOW ALL WORK AND JUSTIFY ALL ANSWERS. 1. We will graph linear inequalities first. Let us first consider 2 + 6 240 (a) First, we will graph the boundar
Investigation Free Fall
Investigation Free Fall Name Period Date You will need: a motion sensor, a small pillow or other soft object What function models the height of an object falling due to the force of gravit? Use a motion
Up and Down or Down and Up
Lesson.1 Skills Practice Name Date Up and Down or Down and Up Eploring Quadratic Functions Vocabular Write the given quadratic function in standard form. Then describe the shape of the graph and whether
SLOPE A MEASURE OF STEEPNESS through 7.1.5
SLOPE A MEASURE OF STEEPNESS 7.1. through 7.1.5 Students have used the equation = m + b throughout this course to graph lines and describe patterns. When the equation is written in -form, the m is the
STRAND I: Geometry and Trigonometry. UNIT 37 Further Transformations: Student Text Contents. Section Reflections. 37.
MEP Jamaica: STRN I UNIT 7 Further Transformations: Student Tet ontents STRN I: Geometr and Trigonometr Unit 7 Further Transformations Student Tet ontents Section 7. Reflections 7. Rotations 7. Translations
Graphing Radical Functions
17 LESSON Graphing Radical Functions Basic Graphs of Radical Functions UNDERSTAND The parent radical function, 5, is shown. 5 0 0 1 1 9 0 10 The function takes the principal, or positive, square root of.
Transformations of y = x 2 Parent Parabola
Transformations of = 2 SUGGESTED LEARNING STRATEGIES: Marking the Tet, Interactive Word Wall, Create Representations, Quickwrite 1. Graph the parent quadratic function, f () = 2, on the coordinate grid
Name: Date: Practice Final Exam Part II covering sections a108. As you try these problems, keep referring to your formula sheet.
Name: Date: Practice Final Eam Part II covering sections 9.1-9.4 a108 As ou tr these problems, keep referring to our formula sheet. 1. Find the standard form of the equation of the circle with center at
REVIEW, pages
REVIEW, pages 330 335 4.1 1. a) Use a table of values to graph = + 6-8. -5-4 -3 - -1 0 1 1 0-8 -1-1 -8 0 1 6 8 8 0 b) Determine: i) the intercepts ii) the coordinates of the verte iii) the equation of
CHAPTER 9: Quadratic Equations and Functions
Notes # CHAPTER : Quadratic Equations and Functions -: Exploring Quadratic Graphs A. Intro to Graphs of Quadratic Equations: = ax + bx + c A is a function that can be written in the form = ax + bx + c
Study Skills Exercise. Review Exercises. Concept 1: Linear and Constant Functions
Section. Graphs of Functions Section. Boost our GRADE at mathzone.com! Stud Skills Eercise Practice Eercises Practice Problems Self-Tests NetTutor e-professors Videos. Define the ke terms. a. Linear function
Midpoint and Distance Formulas
Midpoint and Distance Formulas Find the midpoint of a segment on the coordinate plane. Find the distance between two points on the coordinate plane. Fremont are the Midpoint and Distance Formulas used
8.5. Quadratic Function A function f is a quadratic function if f(x) ax 2 bx c, where a, b, and c are real numbers, with a 0.
8.5 Quadratic Functions, Applications, and Models In the previous section we discussed linear functions, those that are defined b firstdegree polnomials. In this section we will look at quadratic functions,
9. f(x) = x f(x) = x g(x) = 2x g(x) = 5 2x. 13. h(x) = 1 3x. 14. h(x) = 2x f(x) = x x. 16.
Section 4.2 Absolute Value 367 4.2 Eercises For each of the functions in Eercises 1-8, as in Eamples 7 and 8 in the narrative, mark the critical value on a number line, then mark the sign of the epression
2.1 Transformers: Shifty y s A Develop Understanding Task
3 2.1 Transformers: Shifty y s A Develop Understanding Task Optima is designing a robot quilt for her new grandson. She plans for the robot to have a square face. The amount of fabric that she needs for
2.3. Horizontal and Vertical Translations of Functions. Investigate
.3 Horizontal and Vertical Translations of Functions When a video game developer is designing a game, she might have several objects displaed on the computer screen that move from one place to another
Module 2, Section 2 Graphs of Trigonometric Functions
Principles of Mathematics Section, Introduction 5 Module, Section Graphs of Trigonometric Functions Introduction You have studied trigonometric ratios since Grade 9 Mathematics. In this module ou will
Unit 5 Lesson 2 Investigation 1
Name: Investigation 1 Modeling Rigid Transformations CPMP-Tools Computer graphics enable designers to model two- and three-dimensional figures and to also easil manipulate those figures. For eample, interior
Lesson/Unit Plan Name: Comparing Linear and Quadratic Functions. Timeframe: 50 minutes + up to 60 minute assessment/extension activity
Grade Level/Course: Algebra 1 Lesson/Unit Plan Name: Comparing Linear and Quadratic Functions Rationale/Lesson Abstract: This lesson will enable students to compare the properties of linear and quadratic
Section 4.4: Parabolas
Objective: Graph parabolas using the vertex, x-intercepts, and y-intercept. Just as the graph of a linear equation y mx b can be drawn, the graph of a quadratic equation y ax bx c can be drawn. The graph
Unit 4: Part 1 Graphing Quadratic Functions
Name: Block: Unit : Part 1 Graphing Quadratic Functions Da 1 Graphing in Verte Form & Intro to Quadratic Regression Da Graphing in Intercept Form Da 3 Da Da 5 Da Graphing in Standard Form Review Graphing
Warm-Up Exercises. Find the x-intercept and y-intercept 1. 3x 5y = 15 ANSWER 5; y = 2x + 7 ANSWER ; 7
Warm-Up Exercises Find the x-intercept and y-intercept 1. 3x 5y = 15 ANSWER 5; 3 2. y = 2x + 7 7 2 ANSWER ; 7 Chapter 1.1 Graph Quadratic Functions in Standard Form A quadratic function is a function that
1. y = f(x) y = f(x + 3) 3. y = f(x) y = f(x 1) 5. y = 3f(x) 6. y = f(3x) 7. y = f(x) 8. y = f( x) 9. y = f(x 3) + 1
.7 Transformations.7. Eercises To see all of the help resources associated with this section, click OSttS Chapter b. Suppose (, ) is on the graph of = f(). In Eercises - 8, use Theorem.7 to find a point
4 B. 4 D. 4 F. 3. What are some common characteristics of the graphs of cubic and quartic polynomial functions?
.1 Graphing Polnomial Functions COMMON CORE Learning Standards HSF-IF.B. HSF-IF.C.7c Essential Question What are some common characteristics of the graphs of cubic and quartic polnomial functions? A polnomial
Domain of Rational Functions
SECTION 46 RATIONAL FU NCTIONS SKI LLS OBJ ECTIVES Find the domain of a rational function Determine vertical, horizontal, and slant asmptotes of rational functions Graph rational functions CONCE PTUAL
Quadratic Functions In Standard Form In Factored Form In Vertex Form Transforming Graphs. Math Background
Graphing In Standard Form In Factored Form In Vertex Form Transforming Graphs Math Background Previousl, ou Identified and graphed linear functions Applied transformations to parent functions Graphed quadratic
2) f (x) = x 2 6x ) y = 1 2 (x 3)
-- w lx0zts 0KuUtoaO Sqo5ftswa7rseL ULJLrCw.p FAlrlU ricghitssd jrieqshelr hvheydq.o n 5MoadweP OwgiFtthM BI7nnfuinNi7t7eH AglPgevbwrWan gf.t Worksheet b Kuta Software LLC Algebra /Trig ID: Name Graphing
Rotate. A bicycle wheel can rotate clockwise or counterclockwise. ACTIVITY: Three Basic Ways to Move Things
. Rotations object in a plane? What are the three basic was to move an Rotate A biccle wheel can rotate clockwise or counterclockwise. 0 0 0 9 9 9 8 8 8 7 6 7 6 7 6 ACTIVITY: Three Basic Was to Move Things
Making Graphs from a Table of Values and Understanding the Graphs of Horizontal and Vertical Lines Blue Level Problems
Making Graphs from a Table of Values and Understanding the Graphs of Horizontal and Vertical Lines Blue Level Problems. Coordinate Triangle? We have a triangle ABC, and it has an area of units^. Point
Worksheet: Transformations of Quadratic Functions
Worksheet: Transformations of Quadratic Functions Multiple Choice Identif the choice that best completes the statement or answers the question.. Which correctl identifies the values of the parameters a,
2-3. Attributes of Absolute Value Functions. Key Concept Absolute Value Parent Function f (x)= x VOCABULARY TEKS FOCUS ESSENTIAL UNDERSTANDING
- Attributes of Absolute Value Functions TEKS FOCUS TEKS ()(A) Graph the functions f() =, f() =, f() =, f() =,f() = b, f() =, and f() = log b () where b is,, and e, and, when applicable, analze the ke
3.2 Polynomial Functions of Higher Degree
71_00.qp 1/7/06 1: PM Page 6 Section. Polnomial Functions of Higher Degree 6. Polnomial Functions of Higher Degree What ou should learn Graphs of Polnomial Functions You should be able to sketch accurate
of Straight Lines 1. The straight line with gradient 3 which passes through the point,2
Learning Enhancement Team Model answers: Finding Equations of Straight Lines Finding Equations of Straight Lines stud guide The straight line with gradient 3 which passes through the point, 4 is 3 0 Because
2.4 Polynomial and Rational Functions
Polnomial Functions Given a linear function f() = m + b, we can add a square term, and get a quadratic function g() = a 2 + f() = a 2 + m + b. We can continue adding terms of higher degrees, e.g. we can
UNIT 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:
Graphing Polynomial Functions
LESSON 7 Graphing Polnomial Functions Graphs of Cubic and Quartic Functions UNDERSTAND A parent function is the most basic function of a famil of functions. It preserves the shape of the entire famil.
Further Differentiation
Worksheet 39 Further Differentiation Section Discriminant Recall that the epression a + b + c is called a quadratic, or a polnomial of degree The graph of a quadratic is called a parabola, and looks like
Module 3: Graphing Quadratic Functions
Haberman MTH 95 Section V Quadratic Equations and Functions Module 3 Graphing Quadratic Functions In this module, we'll review the graphing quadratic functions (you should have studied the graphs of quadratic
TIPS4RM: MHF4U: Unit 1 Polynomial Functions
TIPSRM: MHFU: Unit Polnomial Functions 008 .5.: Polnomial Concept Attainment Activit Compare and contrast the eamples and non-eamples of polnomial functions below. Through reasoning, identif attributes
Algebra 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
Answers. Chapter 4. Cumulative Review Chapters 1 3, pp Chapter Self-Test, p Getting Started, p a) 49 c) e)
. 7" " " 7 "7.. "66 ( ") cm. a, (, ), b... m b.7 m., because t t has b ac 6., so there are two roots. Because parabola opens down and is above t-ais for small positive t, at least one of these roots is