2.2 Transformers: More Than Meets the y’s

Slides:

Advertisements

Similar presentations

The Graph of a Quadratic Function

Advertisements

Quadratic Functions and Their Properties

12-4 Quadratic Functions CA Standards 21.0 and 22.0 CA Standards 21.0 and 22.0 Graph quadratic functions; know that their roots are the x-intercepts; use.

1 Transformations of Functions SECTION Learn the meaning of transformations. Use vertical or horizontal shifts to graph functions. Use reflections.

Quadratic Functions Section 2.2. Objectives Rewrite a quadratic function in vertex form using completing the square. Find the vertex of a quadratic function.

Section 4.1: Vertex Form LEARNING TARGET: I WILL GRAPH A PARABOLA USING VERTEX FORM.

Copyright © Cengage Learning. All rights reserved. Quadratic Equations, Quadratic Functions, and Complex Numbers 9.

Chapter 4 Review. What shape does a Quadratic Function make What shape does a Quadratic Function make when it is graphed? when it is graphed?1. 2. What.

To introduce the general form of a quadratic equation To write quadratic equations that model real-world data To approximate the x-intercepts and other.

1. Determine if f(x) has a minimum or maximum 2. Find the y-intercept of f(x) 3. Find the equation of the axis of symmetry of f(x) 4. Find the vertex of.

Quadratic Functions. The graph of any quadratic function is called a parabola. Parabolas are shaped like cups, as shown in the graph below. If the coefficient.

Copyright © 2011 Pearson Education, Inc. Quadratic Functions and Inequalities Section 3.1 Polynomial and Rational Functions.

Goal: Graph quadratic functions in different forms.

Quadratic Functions Objectives: Graph a Quadratic Function using Transformations Identify the Vertex and Axis of Symmetry of a Quadratic Function Graph.

Section 9-5: Parabolas Recall that Parabola will result in a U shape curve. In chapter 5 we looked at Parabolas that opened up or down, now we will look.

Graphical Transformations

Algebra I Chapter 8/9 Notes. Section 8-1: Adding and Subtracting Polynomials, Day 1 Polynomial – Binomial – Trinomial – Degree of a monomial – Degree.

Warm Up Tuesday, 8/11 Describe the transformation, then graph the function. 1) h(x)= (x + 9) ) g(x) = -5x Write the resulting equation.

Topics: Standard and Vertex form of a Quadratic Function Finding Key Features of a Quadratic algebraically and graphically. Graphing Quadratics.

Section 2.7 – Absolute Value The table shows the numbers of hours students spent online the day before a test and the scores on the test. Make a scatter.

Quadratics Review Day 1. Multiplying Binomials Identify key features of a parabola Describe transformations of quadratic functions Objectives FOILFactored.

Graphing Quadratic Equations Standard Form & Vertex Form.

Graphing Quadratic Equations

Ch. 4 Pre-test 1.Graph the function : y = – 4x 2 Then label the vertex and axis of symmetry. 2.Write the quadratic function in standard form : y = (x –

6.1 Graphing Quadratic Functions Parabola Axis of symmetry Vertex.

Graphing Quadratic Functions (2.1.1) October 1st, 2015.

2.3 Quadratic Functions. A quadratic function is a function of the form:

Coordinate System Graphing and Ordering Pairs. Coordinate Plane X - Axis Y - Axis Origin Quadrant 1 Quadrant 4Quadrant 3 Quadrant 2.

Chapter 6-1 Graphing Quadratic Functions. Which of the following are quadratic functions?

Solving Quadratic Equations by Graphing 4 Lesson 10.2.

Transformations Review Vertex form: y = a(x – h) 2 + k The vertex form of a quadratic equation allows you to immediately identify the vertex of a parabola.

6.6 Analyzing Graphs of Quadratic Functions. The vertex form of a quadratic function gives us certain information that makes it very easy to graph the.

4.1 – 4.3 Review. Sketch a graph of the quadratic. y = -(x + 3) Find: Vertex (-3, 5) Axis of symmetry x = -3 y - intercept (0, -4) x - intercepts.

QUADRATIC FUNCTIONS. Transform quadratic functions. Describe the effects of changes in the coefficients of y = a(x – h)² + k. Objectives quadratic function.

Unit 3-1: Graphing Quadratic Functions Learning Target: I will graph a quadratic equation and label its key features.

2.1 Transformers: Shifty y’s

Essential Question: How do you graph a quadratic function in vertex and intercept form? Students will write a summary on the steps to graphing quadratic.

Do Now: Solve the equation in the complex number system.

Quadratic Functions. 1. The graph of a quadratic function is given. Choose which function would give you this graph:

Do Now: Solve the equation in the complex number system.

Write each expression in standard polynomial form. Welcome! Pick up a new notes, then complete the problems below

Chapter 4: Polynomials Quadratic Functions (Section 4.1)

Unit 2 – Quadratic Functions & Equations. A quadratic function can be written in the form f(x) = ax 2 + bx + c where a, b, and c are real numbers and.

SOLVING QUADRATIC EQUATIONS A.4c: The student will solve multi-step linear and quadratic equations in two variables, including…solving quadratic equations.

Algebra I Final Exam Review. Simplify Answer: Write an exponential function which models the table below. XY

2.1 Quadratic Functions Standard form Applications.

4.1/4.2 Graphing Quadratic Functions in Vertex or Intercept Form Definitions Definitions 3 Forms 3 Forms Steps for graphing each form Steps for graphing.

Factor each polynomial.

Algebra I Chapter 8/9 Notes.

Warm Up Describe the transformation, then graph the function.

Warm Up /05/17 1. Evaluate x2 + 5x for x = -4 and x = 3. __; ___

Quadratic Functions Transformational Form

$$$ DEAL OR NO DEAL $$$.

Warm Up Describe the transformation, then graph the function.

Parabolas 4.2. Parabolas 4.2 Standard Form of Parabolic Equations Standard Form of Equation Axis of Symmetry Vertex Direction Parabola Opens up or.

Quadratic Functions.

Graph Quadratic Functions in Standard Form

Creating & Graphing Quadratic Functions Using Vertex Form (3.3.3)

Section 9.1 Day 2 Graphing Quadratic Functions

I can write the equation of a

Graphs of Quadratic Functions Part 1

MATH 1310 Section 3.5.

Section 10.2 “Graph y = ax² + bx + c”

Algebra 2 – Chapter 6 Review

MATH 1310 Section 3.5.

Calculate points from this table and plot the points as you go.

10.1: Quadratic Equations and Functions

Presentation transcript:

2.2 Transformers: More Than Meets the y’s A Solidify Understanding Task Prior Knowledge: 4 Transformations Begin with the Parent function Description of Transformation Change to function Change to coordinates Translate down 3 Multiply by 3 Add 3 to x-coordinates Reflect x-axis Replace x with –x

Small Groups Whole group 1st problem. Pairs complete 2nd problem. 3rd problem one person works problem and explains, other person questions 4th problem reverse roles of problem 3 and be prepared to present List the transformations, move and plot 3 points to create a graph, label vertex. Describe transformation and how it changes points. Graph the parent function and identify 3 points. Change the 3 points. Graph the new points to create graph. Explain how you can find the vertex and the axis of symmetry in the equation.

Write the equation for each problem below. Use a second representation Write the equation for each problem below. Use a second representation. Choices: table, graph, equation. The area of a square with side length x, where the side length is decreased by 3, the area is multiplied by 2 and then 4 square units are added to the area. 3. 2. x f(x) -4 7 -3 2 -2 -1 1 3 14 4 23

4.

Graph each equation without using technology. List the transformations Graph each equation without using technology. List the transformations. Be sure to have the exact vertex and at least two correct points on either side of the line of symmetry. 5. f (𝑥) = −𝑥2 + 3 6. g(𝑥) = (𝑥+ 2)2 − 5 7. ℎ(𝑥) = 3(𝑥− 1)2 + 2

8. Given: f (𝑥) = 𝑎(𝑥− ℎ)2 + 𝑘 What point is the vertex of the parabola? What is the equation of the line of symmetry? How can you tell if the parabola opens up or down? How do you identify the dilation? Does it matter in which order the transformations are done? Explain why or why not with an example?

Computational skills: Multiplying binomials Def) binomial – Complete Ready of Section 2.2

Complete Set of Section 2.2 Problems 12-17

14 NAME Structures of Expressions 2.2 Go Use the table to identify the vertex, the equation for the axis of symmetry, and state the number of x-intercept(s) the parabola will have, if any. Will the vertex be a minimum or a maximum? 26. vertex A.S. x - intercept max or min?