Writing Equivalent Forms of Quadratic Functions Adapted from Walch Education
|
|
- Erin McKinney
- 5 years ago
- Views:
Transcription
1 Writing Equivalent Forms of Quadratic Functions Adapted from Walch Education
2 Recall The standard form, or general form, of a quadratic function is written as f(x) = ax 2 + bx + c, where a is the coefficient of the quadratic term, b is the coefficient of the linear term, and c is the constant term. The process of completing the square can be used to transform a quadratic equation from standard form to vertex form, f(x) = a(x h) 2 + k. Vertex form can be used to identify the key features of a function s graph. 2
3 And The vertex of a parabola is the point where the graph changes from increasing to decreasing, or vice versa. In vertex form, the extremum of the graph of a quadratic equation is easily identified using the vertex, (h, k). If a < 0, the function achieves a maximum, where k is the y- coordinate of the maximum and h is the x-coordinate of the maximum. If a > 0, the function has a minimum, where k is the y- coordinate of the minimum and h is the x-coordinate of the minimum. 3
4 Don t forget, Because the axis of symmetry goes through the vertex, the axis of symmetry is easily identified from vertex form as x = h. The process of factoring can be used to transform a quadratic equation in standard form to factored form, f(x) = a(x r)(x s). The zeros of a function are the x-values where the function value is 0. Setting the factored form equal to 0, 0 = a(x r)(x s), the zeros are easily identified as r and s. 4
5 One more thing The axis of symmetry is easily identified from the factored form as the axis of symmetry occurs at the midpoint between the zeros. Therefore, the axis of symmetry is x = r + s 2. 5
6 Practice # 1 Suppose that the flight of a launched bottle rocket can be modeled by the equation y = x 2 + 6x, where y measures the rocket s height above the ground in meters and x represents the rocket s horizontal distance in meters from the launching spot at x = 0. How far does the bottle rocket travel in the horizontal direction from launch to landing? What is the maximum height the bottle rocket reaches? How far has the bottle rocket traveled horizontally when it reaches its maximum height? 6
7 Identify the zeros of the function In the original equation, y represents the height of the bottle rocket. At launch and landing, the height of the bottle rocket is 0. Write the original equation in factored form. Set it equal to 0 to identify the zeros of the function. 7
8 Continued, y = x 2 + 6x Original equation 0 = x 2 + 6x Set the equation equal to 0. 0 = (x 2 6x) Factor out 1. 0 = x(x 6) Factor the binomial. Solve for x by setting each factor equal to 0. x = 0 or x 6 = 0 x = 0 or x = 6 8
9 Continued, The x-intercepts are at x = 0 and x = 6. Find the distance between the two points to determine how far the bottle rocket travels in the horizontal direction. 6 0 = 6 The bottle rocket travels 6 meters in the horizontal direction from launch to landing. 9
10 Determine the maximum height of the bottle rocket The maximum height occurs at the vertex. Write the equation in vertex form by completing the square. 10
11 Continued, y = x 2 + 6x y = (x 2 6x) y = (x 2 6x + 9) + 9 y = (x 3) Original equation Factor out the common factor, 1, from the variable terms. Add and subtract the square of 1 of the x-term. Be sure to 2 multiply the subtracted term by a, 1. Write the trinomial as a binomial squared and simplify the constant term. 11
12 Continued, The vertex form is y = (x 3) The vertex is (3, 9). The maximum value is the y-coordinate of the vertex, 9. The bottle rocket reaches a maximum height of 9 meters. 12
13 Determine the horizontal distance from the launch point to the maximum height of the bottle rocket. We know that the bottle rocket is launched from the point (0, 0) and reaches a maximum height at (3, 9). Subtract the x-values of the two points to find the distance traveled horizontally. 3 0 = 3 13
14 Continued, Another method is to take the total distance traveled horizontally from launch to landing and divide it by 2 to find the same answer. This is because the maximum value occurs halfway between the zeros of the function. 6 2 = 3 The bottle rocket has traveled 3 meters horizontally when it reaches its maximum height. 14
15 Dr. Dambreville Thanks for Watching!!!
Lesson 1: Analyzing Quadratic Functions
UNIT QUADRATIC FUNCTIONS AND MODELING Lesson 1: Analyzing Quadratic Functions Common Core State Standards F IF.7 F IF.8 Essential Questions Graph functions expressed symbolically and show key features
More informationReplacing f(x) with k f(x) and. Adapted from Walch Education
Replacing f(x) with k f(x) and f(k x) Adapted from Walch Education Graphing and Points of Interest In the graph of a function, there are key points of interest that define the graph and represent the characteristics
More informationUNIT 5 QUADRATIC FUNCTIONS Lesson 6: Analyzing Quadratic Functions Instruction
Prerequisite Skills This lesson requires the use of the following skills: factoring quadratic expressions finding the vertex of a quadratic function Introduction We have studied the key features of the
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 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 information6.4 Vertex Form of a Quadratic Function
6.4 Vertex Form of a Quadratic Function Recall from 6.1 and 6.2: Standard Form The standard form of a quadratic is: f(x) = ax 2 + bx + c or y = ax 2 + bx + c where a, b, and c are real numbers and a 0.
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 informationMore Ways to Solve & Graph Quadratics The Square Root Property If x 2 = a and a R, then x = ± a
More Ways to Solve & Graph Quadratics The Square Root Property If x 2 = a and a R, then x = ± a Example: Solve using the square root property. a) x 2 144 = 0 b) x 2 + 144 = 0 c) (x + 1) 2 = 12 Completing
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 informationChapter 6 Practice Test
MPM2D Mr. Jensen Chapter 6 Practice Test Name: Standard Form 2 y= ax + bx+ c Factored Form y= a( x r)( x s) Vertex Form 2 y= a( x h) + k Quadratic Formula ± x = 2 b b 4ac 2a Section 1: Multiply Choice
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 informationWarm-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
More informationQuadratics and their Properties
Algebra 2 Quadratics and their Properties Name: Ms. Williams/Algebra 2 Pd: 1 Table of Contents Day 1: COMPLETING THE SQUARE AND SHIFTING PARABOLAS SWBAT: Write a quadratic from standard form to vertex
More informationSection 7.2 Characteristics of Quadratic Functions
Section 7. Characteristics of Quadratic Functions A QUADRATIC FUNCTION is a function of the form " # $ N# 1 & ;# & 0 Characteristics Include:! Three distinct terms each with its own coefficient:! An x
More informationReview for Quarter 3 Cumulative Test
Review for Quarter 3 Cumulative Test I. Solving quadratic equations (LT 4.2, 4.3, 4.4) Key Facts To factor a polynomial, first factor out any common factors, then use the box method to factor the quadratic.
More information2.2 Transformers: More Than Meets the y s
10 SECONDARY MATH II // MODULE 2 STRUCTURES OF EXPRESSIONS 2.2 Transformers: More Than Meets the y s A Solidify Understanding Task Writetheequationforeachproblembelow.Useasecond representationtocheckyourequation.
More informationSection 6.2 Properties of Graphs of Quadratic Functions soln.notebook January 12, 2017
Section 6.2: Properties of Graphs of Quadratic Functions 1 Properties of Graphs of Quadratic Functions A quadratic equation can be written in three different ways. Each version of the equation gives information
More informationQuadratic Functions, Part 1
Quadratic Functions, Part 1 A2.F.BF.A.1 Write a function that describes a relationship between two quantities. A2.F.BF.A.1a Determine an explicit expression, a recursive process, or steps for calculation
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 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 informationProperties of Quadratic functions
Name Today s Learning Goals: #1 How do we determine the axis of symmetry and vertex of a quadratic function? Properties of Quadratic functions Date 5-1 Properties of a Quadratic Function A quadratic equation
More informationAmplifying an Instructional Task Algebra II Example
Original Task The student is expected to write the equation of a parabola using given attributes, including vertex, focus, directrix, axis of symmetry, and direction of opening. A(4)(B) Write the equations
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 informationMath 2201 Unit 4: Quadratic Functions. 16 Hours
Math 2201 Unit 4: Quadratic Functions 16 Hours 6.1: Exploring Quadratic Relations Quadratic Relation: A relation that can be written in the standard form y = ax 2 + bx + c Ex: y = 4x 2 + 2x + 1 ax 2 is
More informationMAC Learning Objectives. Module 4. Quadratic Functions and Equations. - Quadratic Functions - Solving Quadratic Equations
MAC 1105 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. 2. Complete
More information9.1: GRAPHING QUADRATICS ALGEBRA 1
9.1: GRAPHING QUADRATICS ALGEBRA 1 OBJECTIVES I will be able to graph quadratics: Given in Standard Form Given in Vertex Form Given in Intercept Form What does the graph of a quadratic look like? https://www.desmos.com/calculator
More informationStudent Exploration: Quadratics in Polynomial Form
Name: Date: Student Exploration: Quadratics in Polynomial Form Vocabulary: axis of symmetry, parabola, quadratic function, vertex of a parabola Prior Knowledge Questions (Do these BEFORE using the Gizmo.)
More informationBut a vertex has two coordinates, an x and a y coordinate. So how would you find the corresponding y-value?
We will work with the vertex, orientation, and x- and y-intercepts of these functions. Intermediate algebra Class notes More Graphs of Quadratic Functions (section 11.6) In the previous section, we investigated
More information7.1A Investigating Quadratic Functions in Vertex (Standard) Form: y = a(x±p) 2 ±q. Parabolas have a, a middle point. For
7.1A Investigating Quadratic Functions in Vertex (Standard) Form: y = a(x±p) ±q y x Graph y x using a table of values x -3 - -1 0 1 3 Graph Shape: the graph shape is called a and occurs when the equation
More informationParabolas have a, a middle point. For. In this example, the equation of the axis of symmetry is
5.1/5.A Investigating Quadratic Functions in Standard Form: y = a(x ± h) ± k y x Graph y x using a table of values x -3 - -1 0 1 3 Graph Shape: the graph shape is called a and occurs when the equation
More informationEXERCISE SET 10.2 MATD 0390 DUE DATE: INSTRUCTOR
EXERCISE SET 10. STUDENT MATD 090 DUE DATE: INSTRUCTOR You have studied the method known as "completing the square" to solve quadratic equations. Another use for this method is in transforming the equation
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 informationSection 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
More informationAlgebra 1 STAAR EOC Review #9 Reporting Category 5: Quadratic and Other Nonlinear Functions
Name Class Date RC9 A.09B Algebra 1 STAAR EOC Review #9 Reporting Category 5: Quadratic and Other Nonlinear Functions 1. Which shows the functions correctly listed in order from widest to narrowest graph?
More informationQuadratic Functions CHAPTER. 1.1 Lots and Projectiles Introduction to Quadratic Functions p. 31
CHAPTER Quadratic Functions Arches are used to support the weight of walls and ceilings in buildings. Arches were first used in architecture by the Mesopotamians over 4000 years ago. Later, the Romans
More informationQUADRATIC FUNCTIONS TEST REVIEW NAME: SECTION 1: FACTORING Factor each expression completely. 1. 3x p 2 16p. 3. 6x 2 13x 5 4.
QUADRATIC FUNCTIONS TEST REVIEW NAME: SECTION 1: FACTORING Factor each expression completely. 1. 3x 2 48 2. 25p 2 16p 3. 6x 2 13x 5 4. 9x 2 30x + 25 5. 4x 2 + 81 6. 6x 2 14x + 4 7. 4x 2 + 20x 24 8. 4x
More informationSection 3.3. Analyzing Graphs of Quadratic Functions
Section 3.3 Analyzing Graphs of Quadratic Functions Introduction Definitions A quadratic function is a function with the form f (x) = ax 2 + bx + c, where a 0. Definitions A quadratic function is a function
More informationF.BF.B.3: Graphing Polynomial Functions
F.BF.B.3: Graphing Polynomial Functions 1 Given the graph of the line represented by the equation f(x) = 2x + b, if b is increased by 4 units, the graph of the new line would be shifted 4 units 1) right
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 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 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 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 information9.1 Linear Inequalities in Two Variables Date: 2. Decide whether to use a solid line or dotted line:
9.1 Linear Inequalities in Two Variables Date: Key Ideas: Example Solve the inequality by graphing 3y 2x 6. steps 1. Rearrange the inequality so it s in mx ± b form. Don t forget to flip the inequality
More informationFor every input number the output involves squaring a number.
Quadratic Functions The function For every input number the output involves squaring a number. eg. y = x, y = x + 3x + 1, y = 3(x 5), y = (x ) 1 The shape parabola (can open up or down) axis of symmetry
More informationApplied Parabolas: Catapult (one test grade)
Name: I. Overview: PreCalculus Applied Parabola Project Applied Parabolas: Catapult (one test grade) You will use catapults to launch candy into the air. Using a stopwatch, you will time how long the projectile
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 informationParabolas have a, a middle point. For
Key Ideas: 3.1A Investigating Quadratic Functions in Vertex Form: y = a(x ± p) ± q Date: Graph y x using the count method. Quick way to graph: Use a basic count: Start at vertex: in this case (0,0) Graph
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. The diagram shows part of the graph of y = a (x h) 2 + k. The graph has its vertex at P, and passes through the point A with coordinates (1, 0).
Quadratics Vertex Form 1. Part of the graph of the function y = d (x m) + p is given in the diagram below. The x-intercepts are (1, 0) and (5, 0). The vertex is V(m, ). (a) Write down the value of (i)
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 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 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 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 informationUnit 2 Day 5. Characteristics of Quadratic Functions
Unit 2 Day 5 Characteristics of Quadratic Functions 1 Warm Up 1.) Jason and Jim jumped off a cliff into the ocean in Acapulco while vacationing. Jason s height as a function of time could be modeled by
More informationWorking with Quadratic Functions in Standard and Vertex Forms
Working with Quadratic Functions in Standard and Vertex Forms Example 1: Identify Characteristics of a Quadratic Function in Standard Form f( x) ax bx c, a 0 For the quadratic function f( x) x x 3, identify
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 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 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 informationMission 1 Graph Quadratic Functions in Standard Form
Algebra Unit 4 Graphing Quadratics Name Quest Mission 1 Graph Quadratic Functions in Standard Form Objectives: Graph functions expressed symbolically by hand and show key features of the graph, including
More information2.1 Quadraticsnts.notebook. September 10, 2018
1 A quadratic function is a polynomial function of second degree. The graph of a quadratic function is called a parabola. 2 Standard Form: Intercept Form: Vertex Form: f(x) = a(x h) 2 + k vertex: (h, k)
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 informationWHAT ARE THE PARTS OF A QUADRATIC?
4.1 Introduction to Quadratics and their Graphs Standard Form of a Quadratic: y ax bx c or f x ax bx c. ex. y x. Every function/graph in the Quadratic family originates from the parent function: While
More informationQuiz 1 Review: Quadratics through 4.2.2
Name: Class: Date: ID: A Quiz 1 Review: Quadratics 4.1.1 through 4.2.2 Graph each function. How is each graph a translation of f(x) = x 2? 1. y = x 2 + 2 2. y = (x 3) 2 3. y = (x + 3) 2 + 4 4. Which is
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 (Section 2-1)
Quadratic Functions (Section 2-1) Section 2.1, Definition of Polynomial Function f(x) = a is the constant function f(x) = mx + b where m 0 is a linear function f(x) = ax 2 + bx + c with a 0 is a quadratic
More informationUnit 3, Lesson 3.1 Creating and Graphing Equations Using Standard Form
Unit 3, Lesson 3.1 Creating and Graphing Equations Using Standard Form Imagine the path of a basketball as it leaves a player s hand and swooshes through the net. Or, imagine the path of an Olympic diver
More informationGSE Algebra 1 Name Date Block. Unit 3b Remediation Ticket
Unit 3b Remediation Ticket Question: Which function increases faster, f(x) or g(x)? f(x) = 5x + 8; two points from g(x): (-2, 4) and (3, 10) Answer: In order to compare the rate of change (roc), you must
More information3.1 Quadratic Functions and Models
3.1 Quadratic Functions and Models Objectives: 1. Identify the vertex & axis of symmetry of a quadratic function. 2. Graph a quadratic function using its vertex, axis and intercepts. 3. Use the maximum
More informationSect 3.1 Quadratic Functions and Models
Objective 1: Sect.1 Quadratic Functions and Models Polynomial Function In modeling, the most common function used is a polynomial function. A polynomial function has the property that the powers of the
More informationUNIT 5 QUADRATIC FUNCTIONS Lesson 7: Building Functions Instruction
Prerequisite Skills This lesson requires the use of the following skills: multiplying linear expressions factoring quadratic equations finding the value of a in the vertex form of a quadratic equation
More informationLecture 5. If, as shown in figure, we form a right triangle With P1 and P2 as vertices, then length of the horizontal
Distance; Circles; Equations of the form Lecture 5 y = ax + bx + c In this lecture we shall derive a formula for the distance between two points in a coordinate plane, and we shall use that formula to
More informationModule 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
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 information3.1 Quadratic Functions in Vertex Form
3.1 Quadratic Functions in Vertex Form 1) Identify quadratic functions in vertex form. 2) Determine the effect of a, p, and q on the graph of a quadratic function in vertex form where y = a(x p)² + q 3)
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 information13.1 2/20/2018. Conic Sections. Conic Sections: Parabolas and Circles
13 Conic Sections 13.1 Conic Sections: Parabolas and Circles 13.2 Conic Sections: Ellipses 13.3 Conic Sections: Hyperbolas 13.4 Nonlinear Systems of Equations 13.1 Conic Sections: Parabolas and Circles
More information2. From General Form: y = ax 2 + bx + c # of x-intercepts determined by the, D =
Alg2H 5-3 Using the Discriminant, x-intercepts, and the Quadratic Formula WK#6 Lesson / Homework --Complete without calculator Read p.181-p.186. Textbook required for reference as well as to check some
More informationAlgebra II Chapter 4: Quadratic Functions and Factoring Part 1
Algebra II Chapter 4: Quadratic Functions and Factoring Part 1 Chapter 4 Lesson 1 Graph Quadratic Functions in Standard Form Vocabulary 1 Example 1: Graph a Function of the Form y = ax 2 Steps: 1. Make
More informationProperties of Graphs of Quadratic Functions
H e i g h t (f t ) Lesson 2 Goal: Properties of Graphs of Quadratic Functions Identify the characteristics of graphs of quadratic functions: Vertex Intercepts Domain and Range Axis of Symmetry and use
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 informationSection 9.3 Graphing Quadratic Functions
Section 9.3 Graphing Quadratic Functions A Quadratic Function is an equation that can be written in the following Standard Form., where a 0. Every quadratic function has a U-shaped graph called a. If the
More informationExploring Quadratic Graphs
Exploring Quadratic Graphs The general quadratic function is y=ax 2 +bx+c It has one of two basic graphs shapes, as shown below: It is a symmetrical "U"-shape or "hump"-shape, depending on the sign of
More informationSemester 2 Review Problems will be sectioned by chapters. The chapters will be in the order by which we covered them.
Semester 2 Review Problems will be sectioned by chapters. The chapters will be in the order by which we covered them. Chapter 9 and 10: Right Triangles and Trigonometric Ratios 1. The hypotenuse of a right
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 informationMPM2D. Key Questions & Concepts. Grade 10Math. peace. love. pi.
MPM2D Key Questions & Concepts Grade 10Math peace. love. pi. Unit I: Linear Systems Important Stuff Equations of Lines Slope à Tells us about what the line actually looks like; represented by m; equation
More information5.1 Introduction to the Graphs of Polynomials
Math 3201 5.1 Introduction to the Graphs of Polynomials In Math 1201/2201, we examined three types of polynomial functions: Constant Function - horizontal line such as y = 2 Linear Function - sloped line,
More informationSketching graphs of polynomials
Sketching graphs of polynomials We want to draw the graphs of polynomial functions y = f(x). The degree of a polynomial in one variable x is the highest power of x that remains after terms have been collected.
More informationSlide 2 / 222. Algebra II. Quadratic Functions
Slide 1 / 222 Slide 2 / 222 Algebra II Quadratic Functions 2014-10-14 www.njctl.org Slide 3 / 222 Table of Contents Key Terms Explain Characteristics of Quadratic Functions Combining Transformations (review)
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 informationA I only B II only C II and IV D I and III B. 5 C. -8
1. (7A) Points (3, 2) and (7, 2) are on the graphs of both quadratic functions f and g. The graph of f opens downward, and the graph of g opens upward. Which of these statements are true? I. The graphs
More informationIntegrated Math 1 Honors Module 10 Structures of Expressions Ready, Set, Go! Homework Solutions
1 Integrated Math 1 Honors Module 10 Structures of Expressions Ready, Set, Go! Homework Solutions Adapted from The Mathematics Vision Project: Scott Hendrickson, Joleigh Honey, Barbara Kuehl, Travis Lemon,
More informationY. Butterworth Lehmann & 9.2 Page 1 of 11
Pre Chapter 9 Coverage Quadratic (2 nd Degree) Form a type of graph called a parabola Form of equation we'll be dealing with in this chapter: y = ax 2 + c Sign of a determines opens up or down "+" opens
More informationDo you need a worksheet or a copy of the teacher notes? Go to
Name Period Day Date Assignment (Due the next class meeting) Wednesday Thursday Friday Monday Tuesday Wednesday Thursday Friday Monday Tuesday Wednesday Thursday Friday Monday Tuesday Wednesday Thursday
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 information3.1 Investigating Quadratic Functions in Vertex Form
Math 2200 Date: 3.1 Investigating Quadratic Functions in Vertex Form Degree of a Function - refers to the highest exponent on the variable in an expression or equation. In Math 1201, you learned about
More informationUnit 6 Quadratic Functions
Unit 6 Quadratic Functions 12.1 & 12.2 Introduction to Quadratic Functions What is A Quadratic Function? How do I tell if a Function is Quadratic? From a Graph The shape of a quadratic function is called
More informationMore About Factoring Trinomials
Section 6.3 More About Factoring Trinomials 239 83. x 2 17x 70 x 7 x 10 Width of rectangle: Length of rectangle: x 7 x 10 Width of shaded region: 7 Length of shaded region: x 10 x 10 Area of shaded region:
More informationAlgebra 2 Chapter 2 Practice Test
Algebra 2 Chapter 2 Practice Test 1. Compare the graph of with the graph of. a. The graph of g(x) is a translation 6 units left and 10 units up from the graph of f(x). b. The graph of g(x) is a translation
More informationQUADRATIC FUNCTIONS. PROTOTYPE: f(x) = ax 2 + bx + c. (1) The leading coefficient a 0 is called the shape parameter.
QUADRATIC FUNCTIONS PROTOTYPE: f(x) = ax 2 + bx + c. (1) The leading coefficient a 0 is called the shape parameter. SHAPE-VERTEX FORMULA One can write any quadratic function (1) as f(x) = a(x h) 2 + k,
More informationAlgebra 1 Notes Quarter
Algebra 1 Notes Quarter 3 2014 2015 Name: ~ 1 ~ Table of Contents Unit 9 Exponent Rules Exponent Rules for Multiplication page 6 Negative and Zero Exponents page 10 Exponent Rules Involving Quotients page
More information