Mathematics Parabolas
|
|
- Cori Phillips
- 5 years ago
- Views:
Transcription
1 a place of mind F A C U L T Y O F E D U C A T I O N Department of Curriculum and Pedagog Mathematics Parabolas Science and Mathematics Education Research Group Supported b UBC Teaching and Learning Enhancement Fund
2 Parabolas F D
3 Parabolas I The graph of = x is shown in red. The graph is then shifted units right and 3 units down. Which one of the following equations represents the translated green graph? C. D. E. x x x x x
4 Solution Answer: D Justification: The graph of = x is shifted to the right units b replacing x with (x ). It is shifted down 3 units b replacing with ( + 3). x 3 x x 3 shifts graph, 3 The vertex of = ax is (0, 0). After shifting the graph, the vertex becomes (, 3). In general, the vertex of the equation a x p q is (p, q).
5 Parabolas II What is the vertex of the graph of 8 x 3 15? Is the vertex a maximum or minimum point? C. D. E. 8 15, , , , ,,,,, 15, maximum minimum maximum minimum maximum
6 Solution Answer: C Justification: Recall that the vertex of ax p q is (p, q). Therefore: 8 15 Vertex, 3 The vertex is a maximum because in a , 3 a x p q Since a x p is alwas negative in this case, the graph will open downwards. x
7 Parabolas III The red line shows the graph of = x. All the other lines are in the form: ax In which one of the graphs is 0 a 1? Green graph Blue graph C. Can graph D. Purple graph C. D.
8 Solution Answer: B 0 a 1 Justification: When, the graph of ax is alwas positive so it must lie above (or on) the x- axis. Therefore graph C and D are incorrect. Since a 1, the graph we are looking for must lie below the red graph because its -values are less than. x The correct answer is graph B: 1 x 3 C. D.
9 Parabolas IV Which one of the following is true about a and q if the equation of the given parabola is written in the form a x p q a x p q? C. D. E. a 0, a 0, a 0, a 0, a 0, q 0 q 0 q 0 q 0 q 0
10 Solution Answer: D Justification: The vertex of the graph is at (6, -4). This shows that 3 x 6 4 q 4 0 p 6 This point is a maximum point because the parabolas grows to negative infinit (it opens downwards). Therefore a 0
11 Parabolas V How man solutions are there to the equation 3 0 x 6 4? 3 x 6 4 No solutions 1 solution C. solutions D. Infinite solutions E. Cannot be determined
12 Solution Answer: A Justification: The parabola never crosses the x-axis, which means it has no zeroes. 3 x 6 4 Therefore 3 0 x 6 has no solutions. 4
13 Parabolas VI Which one of the graphs shown has 1 unique zero? D. Red graph Green graph C. Blue graph D. Purple graph E. Can graph C. E.
14 Solution Answer: B (Green) Justification: The vertex of the green graph is located at the point (-5,0). Onl when x = -5 does = 0, so it has 1 zero. Quadratics in the form ax p have 1 zero. The vertices of these quadratics lie on the x- axis at (p,0). C. D. E.
15 Parabolas VII Consider a parabola with a vertex at (, 5) and one x-intercept at., 0 7 What are the coordinates of the other x-intercept? C. D. E. 16,0 7 4, ,0,0, 0
16 Solution Answer: D Justification: The parabola is smmetric around the line x =., 5 The two x-intercepts should therefore be the same distance from the line x =. Distance from x = : Other x-intercept: , , 0
17 Parabolas VIII Consider a parabola with x-intercepts at (0,0) and (-6,0). What are the coordinates of its vertex? C. D. E. 3, 3 6, 0 3, 0 3, 3 Cannotbe determined 6, 0 0, 0
18 Solution Answer: E Justification: It is not possible to determine the -coordinate of the vertex onl knowing two x-intercepts. The answer was therefore Cannot be determined. It is possible to determine the x-value, however. The vertex must located at the midpoint between (-6,0) and (0,0), so its x-coordinate is -3. Both A and B were possible vertices.
19 Parabolas IX Consider a parabola with its vertex at (-3, -3) and one of its x- intercepts at (0, 0). Which one of the following equations represents this parabola? x 3 3 C. D. E. 3 x x x The parabolaisnot unique 3, 3 0, 0
20 Solution Answer: C Justification: The vertex is given so the equation is in the form: 0 ax 3 3 Plugging in the point (0,0) will then find the value for a. a a Note: When points are given and 1 is the vertex, an unique parabola can be found. 1 x , 3 0, 0
21 Parabolas X Consider the graph of the quadratic function: 4 x 3 What is the vertex of the parabola? C. D. E. 4, 3 4, 3 4, 3 4, 3 Noneof the above C. D.
22 Solution Answer: B Justification: Factor out (-1) from (-4-x): 4 x 3 (4 x) 3 This function is the same as 4 x 3, which has a vertex at (-4, 3). The extra negative does not affect the graph due to the square. (Tr expanding the function and completing the square again) C. D.
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
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 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 information2.5: GRAPHS OF EXPENSE AND REVENUE FUNCTIONS OBJECTIVES
Section 2.5: GRAPHS OF EXPENSE AND REVENUE FUNCTIONS OBJECTIVES Write, graph and interpret the expense function. Write, graph and interpret the revenue function. Identify the points of intersection of
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 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 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 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 informationThis 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
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 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 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 informationMathematics Shape and Space: Polygon Angles
a place of mind F A C U L T Y O F E D U C A T I O N Department of Curriculum and Pedagogy Mathematics Shape and Space: Polygon Angles Science and Mathematics Education Research Group Supported by UBC Teaching
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 informationso f can now be rewritten as a product of g(x) = x 2 and the previous piecewisedefined
Version PREVIEW HW 01 hoffman 575) 1 This print-out should have 9 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. FuncPcwise01a 001 10.0
More informationWriting Equivalent Forms of Quadratic Functions Adapted from Walch Education
Writing Equivalent Forms of Quadratic Functions Adapted from Walch Education 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
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 informationName: 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
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 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 informationInvestigating 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
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 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 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 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 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 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 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 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 informationMathematics Geometry: Menger Sponge. Science and Mathematics Education Research Group
F FA ACULTY C U L T Y OF O F EDUCATION E D U C A T I O N Department of Curriculum and Pedagogy Mathematics Geometry: Menger Sponge Science and Mathematics Education Research Group Supported by UBC Teaching
More informationChapter 2. Polynomial and Rational Functions. 2.2 Quadratic Functions
Chapter 2 Polynomial and Rational Functions 2.2 Quadratic Functions 1 /27 Chapter 2 Homework 2.2 p298 1, 5, 17, 31, 37, 41, 43, 45, 47, 49, 53, 55 2 /27 Chapter 2 Objectives Recognize characteristics of
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 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 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 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 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 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 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 informationThe simplest quadratic function we can have is y = x 2, sketched below.
Name: LESSON 6-8 COMPLETING THE SQUARE AND SHIFTING PARABOLAS COMMON CORE ALGEBRA II Date: Parabolas, and graphs more generall, can be moved horizontall and verticall b simple manipulations of their equations.
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 informationUNIT P1: PURE MATHEMATICS 1 QUADRATICS
QUADRATICS Candidates should able to: carr out the process of completing the square for a quadratic polnomial, and use this form, e.g. to locate the vertex of the graph of or to sketch the graph; find
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 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 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 informationSections 3.5, : Quadratic Functions
Week 7 Handout MAC 1105 Professor Niraj Wagh J Sections 3.5, 4.3-4.4: Quadratic Functions A function that can be written in the form f(x)= ax 2 +bx+c for real numbers a, b, and c, with a not equal to zero,
More informationQuadratic 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
More informationCHAPTER 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
More informationQuadratic Functions. Full Set of Notes. No Solutions
Quadratic Functions Full Set of Notes No Solutions Graphing Quadratic Functions The graph of a quadratic function is called a parabola. Applications of Parabolas: http://www.doe.virginia.gov/div/winchester/jhhs/math/lessons/calc2004/appparab.html
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 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 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 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 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 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 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 informationNew Orleans King Cake
New Orleans King Cake A king cake is part of the Mardi Gras tradition in New Orleans. The most traditional king cake is a ring of twisted bread with icing or sugar, usually colored purple, green, and gold
More informationUnit 2: Function Transformation Chapter 1. Basic Transformations Reflections Inverses
Unit 2: Function Transformation Chapter 1 Basic Transformations Reflections Inverses Section 1.1: Horizontal and Vertical Transformations A transformation of a function alters the equation and any combination
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 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 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 informationBLM Answers. BLM 4-1 Prerequisite Skills. BLM 4-3 Section 4.1 Modelling With Quadratic Relations. 10. a)
BLM Answers (page 1) BLM 4-1 Prerequisite Skills 1. a) 11.1 2.7 9.0 d) 20.2 2. a) 1.7 10.7 6.5 d) 25.1 3. a) 9.5 20.7 96 d) 31.85 4. a) 3x 6x 2 + 6x + 5 10x 2 2x + 6 d) 12x 2 + 10x 6 5. a) 5 0 12 d) 2
More informationQuadratic Functions Dr. Laura J. Pyzdrowski
1 Names: (8 communication points) About this Laboratory A quadratic function in the variable x is a polynomial where the highest power of x is 2. We will explore the domains, ranges, and graphs of quadratic
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 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 informationA function: A mathematical relationship between two variables (x and y), where every input value (usually x) has one output value (usually y)
SESSION 9: FUNCTIONS KEY CONCEPTS: Definitions & Terminology Graphs of Functions - Straight line - Parabola - Hyperbola - Exponential Sketching graphs Finding Equations Combinations of graphs TERMINOLOGY
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 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 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 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 information1.1 Graphing Quadratic Functions (p. 2) Definitions Standard form of quad. function Steps for graphing Minimums and maximums
1.1 Graphing Quadratic Functions (p. 2) Definitions Standard form of quad. function Steps for graphing Minimums and maximums Quadratic Function A function of the form y=ax 2 +bx+c where a 0 making a u-shaped
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 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 informationREMARKS. 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
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 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 informationStandard Form of Quadratic Functions
Math Objectives Students will be able to predict how a specific change in the value of a will affect the shape of the graph of the quadratic ax bx c. Students will be able to predict how a specific change
More information8.2 Graph and Write Equations of Parabolas
8.2 Graph and Write Equations of Parabolas Where is the focus and directrix compared to the vertex? How do you know what direction a parabola opens? How do you write the equation of a parabola given the
More informationAugust 29, Quad2b FactoredForm Graphing.notebook
Quadratics 2b Quadratic Function: Graphing Factored Form Standards: F IF.4 & F IF.7 GLOs: #3 Complex Thinker Math Practice: Look for and make use of structure HW: WS #9 (graph on graph paper!) Learning
More information1.1 Functions. Cartesian Coordinate System
1.1 Functions This section deals with the topic of functions, one of the most important topics in all of mathematics. Let s discuss the idea of the Cartesian coordinate system first. Cartesian Coordinate
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 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 informationMathematical Reasoning. Lesson 37: Graphing Quadratic Equations. LESSON 37: Graphing Quadratic Equations
LESSON 37: Graphing Quadratic Equations Weekly Focus: quadratic equations Weekly Skill: graphing Lesson Summary: For the warm-up, students will solve a problem about mean, median, and mode. In Activity
More informationCollege Algebra. Quadratic Functions and their Graphs. Dr. Nguyen October 12, Department of Mathematics UK
College Algebra Quadratic Functions and their Graphs Dr. Nguyen nicholas.nguyen@uky.edu Department of Mathematics UK October 12, 2018 Agenda Quadratic functions and their graphs Parabolas and vertices
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 informationMATH 111 QUADRATICS WORKSHEET. Solution. We can put f(x) into vertex form by completing the square:
MATH 111 QUADRATICS WORKSHEET BLAKE FARMAN UNIVERSITY OF SOUTH CAROLINA Name: Let f(x) = 3x 2 + 6x + 9. Use this function to answer questions Problems 1-3. 1. Write f(x) in vertex form. Solution. We can
More informationDerivatives 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
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 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 informationMath 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
More informationLesson 3: Exploring Quadratic Relations Graphs Unit 5 Quadratic Relations
(A) Lesson Context BIG PICTURE of this UNIT: CONTEXT of this LESSON: How do we analyze and then work with a data set that shows both increase and decrease What is a parabola and what key features do they
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 informationName: -1 and and and and
Roots of Quadratic Equations Studio We ve discussed finding the vertex of a parabola. If we have a quadratic in the form y = a(x h) 2 + k, then the vertex is at the point (h,k), indeed the reason for writing
More information0.4 Family of Functions/Equations
0.4 Family of Functions/Equations By a family of functions, we are referring to a function definition such as f(x) = mx + 2 for m = 2, 1, 1, 0, 1, 1, 2. 2 2 This says, work with all the functions obtained
More informationSystems of Equations and Inequalities. Copyright Cengage Learning. All rights reserved.
5 Systems of Equations and Inequalities Copyright Cengage Learning. All rights reserved. 5.5 Systems of Inequalities Copyright Cengage Learning. All rights reserved. Objectives Graphing an Inequality Systems
More informationDOWNLOAD PDF BIG IDEAS MATH VERTICAL SHRINK OF A PARABOLA
Chapter 1 : BioMath: Transformation of Graphs Use the results in part (a) to identify the vertex of the parabola. c. Find a vertical line on your graph paper so that when you fold the paper, the left portion
More information) 2 + (y 2. x 1. y c x2 = y
Graphing Parabola Parabolas A parabola is a set of points P whose distance from a fixed point, called the focus, is equal to the perpendicular distance from P to a line, called the directrix. Since this
More information2.4 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
More informationWorksheet: 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,
More informationBatman. Part 1 and 2. Sam wants to recreate the Batman symbol using graphs. Describe fully the brown, orange and blue graphs.
Batman Part 1 and 2 Sam wants to recreate the Batman symbol using graphs. Describe fully the brown, orange and blue graphs. Sketch and describe the following graphs teal: y = sinx 14 starting at x = -15
More informationUnit: Quadratic Functions
Unit: Quadratic Functions Learning increases when you have a goal to work towards. Use this checklist as guide to track how well you are grasping the material. In the center column, rate your understand
More information