Section 7.2 Characteristics of Quadratic Functions
|
|
|
- Barrie Horn
- 5 years ago
- Views:
Transcription
1 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 term with coefficient a, where a # 0! An x term with coefficient b! A constant term, c! Note: If any term is missing, the coefficient of that term is 0! The graph of this function is called a parabola! If a > 0, then the parabola opens up; otherwise if a < 0, then the parabola opens down! The y-intercept has coordinates (0, c) Problem 3 WORKED EXAMPLE GRAPHS OF QUADRATIC FUNCTIONS Given the Quadratic Function f (x) x + 4x, complete the table. Identity the coefficients a, b, c a 1, b 4, c Which direction does the parabola open? a 1 which is greater than 0 so parabola opens up What is the y-intercept? c so y-intercept (0, ) Problem 4 MEDIA/CLASS EXAMPLE GRAPHS OF QUADRATIC FUNCTIONS Given the Quadratic Function f(x) x x + 3, complete the table. Identity the coefficients a, b, c Which direction does the parabola open? Why? What is the y-intercept? 38
2 Problem 5 YOU TRY Graph Quadratic Functions Given the Quadratic Function f(x) x 5, complete the table. Identity the coefficients a, b, c Which direction does the parabola open? Why? What is the y-intercept? Vertex of a quadratic function. Given a quadratic function,!!" # $ N# 1 & ;# & 0: The VERTEX is the lowest or highest point (ordered pair) of the parabola. It is the midpoint between the x-intercepts, if they exist.! To find the input value, identify coefficients a and b then compute b! a! Plug this input value into the function to determine the corresponding output value, (i.e. evaluate!" % e ) 1K! The Vertex is always written as an ordered pair. Vertex % e 1K 5 " % e The axis of symmetry is the vertical line that goes through the Vertex, it divides the parabola in half. 1K Problem 6 WORKED EXAMPLE Quadratic Functions: Vertex/Axis Of Symmetry Given the Quadratic Function f (x) x + 4x, complete the table below. Identity the coefficients a, b, c a 1, b 4, c Determine the coordinates of the Vertex. Input Value b x! a (4)! (1)! Output Value f! (! ) ( ) 4! 8!! 6 + 4(! )! Vertex Ordered Pair: (, 6) 39
3 Identify the Axis of Symmetry Equation. Axis of Symmetry: x Sketch the Graph Problem 7 MEDIA/CLASS EXAMPLE Quadratic Functions: Vertex/Axis Of Symmetry Given the Quadratic Function f (x) x x + 3, complete the table, generate a graph of the function, and plot/label the vertex and axis of symmetry on the graph. Identity the coefficients a, b, c Determine the coordinates of the Vertex. Identify the Axis of Symmetry Equation. Graph of the function. Plot/label the vertex and axis of symmetry on the graph. 40
4 Problem 8 YOU TRY Quadratic Functions: Vertex/Axis Of Symmetry Given the Quadratic Function f(x) x 5, complete the table, generate a graph of the function, and plot/label the vertex and axis of symmetry on the graph. Identity the coefficients a, b, c Determine the coordinates of the Vertex. Identify the Axis of Symmetry Equation. Graph of the function. Plot/label the vertex and axis of symmetry on the graph. 41
5 Problem 9 WORKED EXAMPLE Quadratic Functions: Domain and Range Determine the Domain and Range of the Quadratic Function f (x) x + 4x Domain of f(x): All real numbers. & < x < & or ( &, &) Range of f(x): Since the parabola opens upwards, the vertex (, 6) is the lowest point on the graph. The Range is therefore 6! f (x) < & or [ 6, &) Problem 10 MEDIA/CLASS EXAMPLE Quadratic Functions: Domain and Range Determine the Domain and Range of f(x) x 6. Sketch the graph and label the vertex. 4
6 Vertex: Domain of f (x): Range of f (x): Problem 11 YOU TRY Quadratic Functions: Domain and Range Determine the Domain and Range of f (x) x 5. Sketch the graph and label the vertex. Vertex: Domain of f (x): Range of f(x): 43
7 Finding x-intercepts of a Quadratic Function The quadratic function, f (x) ax +bx+c, will have x-intercepts when the graph crosses the x-axis (i.e. when f (x) 0). These points are marked on the graph above as G and H. To find the coordinates of these points, what we are really doing is solving the equation ax +bx+c 0. There are several methods to solve the equations: by factoring, by using the quadratic formula or by completing the square. Problem 1 WORKED EXAMPLE Finding x-intercepts of a Quadratic Function Find the x- intercepts of f (x) x + 4x and plot/label them on the graph. 1. To find the x-intercept, set f(x) 0. That means, solve for x when x + 4x 0.. Equation is not factorable. We will have to either complete the square or use the quadratic formula. If you complete the square: x x + 4x! 0 x + 4x + 4x ( x + ) 6 If you use the quadratic formula, first identify: a 1, b 4, c ( x + ) x x + ± 6 x! ± 6 "! 4. 45,
8 x! 4 ± (4) (1)! 4(1)(! )! 4 ±! 4 ±! 4 ± # 6! 4 ± 6! ± 6 "! 4.45, The x-intercepts are: ( 4.45, 0) and (0.45, 0) 45
9 Problem 13 MEDIA/CLASS EXAMPLE Finding x-intercepts of a Quadratic Function Given the Quadratic Function f (x) x x 6, find the x-intercepts and plot/label them on the graph. Problem 14 YOU TRY Finding x-intercepts of a Quadratic Function Given the Quadratic Function f (x) x 3x 5, find the vertex, x-intercepts, y-intercept, another point symmetric to the y-intercept. Plot and label all of these points on the graph. Then find domain and range. Vertex: (, ) y-intercept: (, ) Point Symmetric to y-intercept: (, ) x-intercepts: (, ) and (, ) Domain: Range: 46
UNIT 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
Lesson 8 Introduction to Quadratic Functions
Lesson 8 Introduction to Quadratic Functions We are leaving exponential and logarithmic functions behind and entering an entirely different world. As you work through this lesson, you will learn to identify
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
Properties 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
Exploring 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
Unit #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
Quadratic 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
3.1 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 + )
WHAT YOU SHOULD LEARN
GRAPHS OF EQUATIONS WHAT YOU SHOULD LEARN Sketch graphs of equations. Find x- and y-intercepts of graphs of equations. Use symmetry to sketch graphs of equations. Find equations of and sketch graphs of
Section 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
WK # 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
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
Quadratic 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
UNIT 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
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:
Quadratic 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,
Unit 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
Chapter 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
Section 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
CHAPTER 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
4.3 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:
9.1: 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
Chapter 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.
Polynomial 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
6.4 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.
Quadratic 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
EXERCISE 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
But 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
2. 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
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
Sect 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
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
F.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
3.1 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
1.1 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
Sections 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,
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
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 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
Writing 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
Section 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,
Sketching 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.
QUADRATIC 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,
2. 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)
2.2 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.
It is than the graph of y= x if a > 1.
Chapter 8 Quadratic Functions and Equations Name: Instructor: 8.1 Quadratic Functions and Their Graphs Graphs of Quadratic Functions Basic Transformations of Graphs More About Graphing Quadratic Functions
GSE 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
Vertex 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
August 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
Quadratics Functions: Review
Quadratics Functions: Review Name Per Review outline Quadratic function general form: Quadratic function tables and graphs (parabolas) Important places on the parabola graph [see chart below] vertex (minimum
MATHS 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
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
2.1 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)
2.5: 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
QUADRATIC 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
Quadratic 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
Properties 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
Algebra 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?
Unit 6 Part I. Quadratic Functions 2/9/2017 2/23/2017
Unit 6 Part I Quadratic Functions 2/9/2017 2/23/2017 By DeviantArt user MagicFiretrucks Name: By the end of this unit, you will be able to Analyze the characteristics of graphs of quadratic functions Graph
) 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
Quadratic 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
Section 18-1: Graphical Representation of Linear Equations and Functions
Section 18-1: Graphical Representation of Linear Equations and Functions Prepare a table of solutions and locate the solutions on a coordinate system: f(x) = 2x 5 Learning Outcome 2 Write x + 3 = 5 as
( )! 1! 3 = x + 1. ( ) =! x + 2
7.5 Graphing Parabolas 1. First complete the square: y = x 2 + 2x! 3 = x 2 + 2x + 1 ( )! 1! 3 = x + 1 ( ) 2! 4 The x-intercepts are 3,1 and the vertex is ( 1, 4). Graphing the parabola: 3. First complete
Section 6.1: Quadratic Functions and their Characteristics Vertical Intercept Vertex Axis of Symmetry Domain and Range Horizontal Intercepts
Lesson 6 Quadratic Functions and Equations Lesson 6 Quadratic Functions and Equations We are leaving exponential functions behind and entering an entirely different world. As you work through this lesson,
Algebra I. Slide 1 / 137. Slide 2 / 137. Slide 3 / 137. Quadratic & Non-Linear Functions. Table of Contents
Slide 1 / 137 Slide 2 / 137 Algebra I Quadratic & Non-Linear Functions 2015-11-04 www.njctl.org Table of Contents Slide 3 / 137 Click on the topic to go to that section Key Terms Explain Characteristics
Student 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.)
3.1 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
Section 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
[The following questions were adapted from Polygraph: Parabolas, Part 2]
![[The following questions were adapted from Polygraph: Parabolas, Part 2]](/thumbs/83/88001318.jpg "[The following questions were adapted from Polygraph: Parabolas, Part 2]")
Opening Exploration 1. Go to https://student.desmos.com and use the class code: to play Polygraph: Parabolas. A description of the game is given below. [The following questions were adapted from https://teacher.desmos.com/activitybuilder/custom/574f12421390db611564fa32#
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
CHAPTER 2. Polynomials and Rational functions
CHAPTER 2 Polynomials and Rational functions Section 2.1 (e-book 3.1) Quadratic Functions Definition 1: A quadratic function is a function which can be written in the form (General Form) Example 1: Determine
Amplifying 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
MAC 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
Plot the points (-1,9) (4,-3), estimate (put a dot) where you think the midpoint is
Algebra Review while 9 th graders are at Club Getaway 1-1 dist and mid pt cw. p. 4 (1,3,5,6,7,8, Hw p. 5 (1-10) Plot the points (-1,9) (4,-3), estimate (put a dot) where you think the midpoint is Find
A 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
5.1 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,
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
QUESTIONS 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
Replacing 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
Lecture 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
10.3 vertex and max values with comparing functions 2016 ink.notebook. March 14, Vertex and Max Value & Page 101.
10.3 vertex and max values with comparing functions 2016 ink.notebook Page 101 Page 102 10.3 Vertex and Value and Comparing Functions Algebra: Transformations of Functions Page 103 Page 104 Lesson Objectives
Chapter 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
Math 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
Quadratics. 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
UNIT 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
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
Unit 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
UNIT 2 QUADRATIC FUNCTIONS AND MODELING Lesson 2: Interpreting Quadratic Functions. Instruction. Guided Practice Example 1
Guided Practice Example 1 A local store s monthly revenue from T-shirt sales is modeled by the function f(x) = 5x 2 + 150x 7. Use the equation and graph to answer the following questions: At what prices
Advanced Math Quadratics Review Name: Dec. 2016
Advanced Math Quadratics Review Name: Dec. 2016 Graph the given quadratic by finding the vertex and building a table around it. Identify the axis of symmetry, maximum or minimum value, domain and range
Introduction to Quadratics
Name: Date: Block: Introduction to Quadratics An quadratic function (parabola) can be expressed in two different forms. Vertex form: Standard form: a( x h) k ax bx c In this activit, ou will see how these
Lesson 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
Quadratics 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
Final Exam Review Algebra Semester 1
Final Exam Review Algebra 015-016 Semester 1 Name: Module 1 Find the inverse of each function. 1. f x 10 4x. g x 15x 10 Use compositions to check if the two functions are inverses. 3. s x 7 x and t(x)
The 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.
Unit: 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
Unit 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
Name: -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
8.2 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
KEY Algebra: Unit 10 Graphing Quadratic Equations & other Relations
Name: KEY Algebra: Unit 10 Graphing Quadratic Equations & other Relations Date: Test Bank Part I: Answer all 15 questions in this part. Each correct answer will receive credits. No partial credit will
MAC Learning Objectives. Transformation of Graphs. Module 5 Transformation of Graphs. - A Library of Functions - Transformation of Graphs
MAC 1105 Module 5 Transformation of Graphs Learning Objectives Upon completing this module, you should be able to: 1. Recognize the characteristics common to families of functions. 2. Evaluate and graph
MAC Module 5 Transformation of Graphs. Rev.S08
MAC 1105 Module 5 Transformation of Graphs Learning Objectives Upon completing this module, you should be able to: 1. Recognize the characteristics common to families of functions. 2. Evaluate and graph