Quadratic Functions, Translation and Reflection

Slides:

Advertisements

Similar presentations

Order of function transformations

Advertisements

Vertical Stretches and Compressions

Transformation of Graphs Tools for Exploration Consider the function f(x) = 0.1(x 3 – 9x 2 ) Enter this function into your calculator on the y=

Using Transformations to Graph Quadratic Functions 5-1

The vertex of the parabola is at (h, k).

Quadratic Functions and Models Lesson 3.1. Nonlinear Data When the points of the function are plotted, they do not lie in a straight line. This graph.

Graphing Quadratics.

Transform quadratic functions.

2.2 b Writing equations in vertex form

Family of Quadratic Functions Lesson 5.5a. General Form Quadratic functions have the standard form y = ax 2 + bx + c  a, b, and c are constants  a ≠

Consider the function: f(x) = 2|x – 2| Does the graph of the function open up or down? 2. Is the graph of the function wider, narrower, or the same.

Function - 2 Meeting 3. Definition of Composition of Functions.

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.

QUADRATIC EQUATIONS in VERTEX FORM y = a(b(x – h)) 2 + k.

Quadratic Functions, Translation and Reflection

5-3 Using Transformations to Graph Quadratic Functions.

Lesson 1.4 Read: Pages Page 48: #1-53 (EOO).

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.

Shifting a Function’s Graph

Lesson 13.3 graphing square root functions

Warm Up For each translation of the point (–2, 5), give the coordinates of the translated point units down 2. 3 units right For each function, evaluate.

Family of Quadratic Functions

WARM UP Use the graph of to sketch the graph of

Do-Now What is the general form of an absolute value function?

Investigation Reflection

13 Algebra 1 NOTES Unit 13.

Using Transformations to Graph Quadratic Functions 5-1

Interesting Fact of the Day

Warm-Up 1. On approximately what interval is the function is decreasing. Are there any zeros? If so where? Write the equation of the line through.

Unit 5 – Quadratics Review Problems

ALGEBRA II ALGEBRA II HONORS/GIFTED - SECTIONS 2-6 and 2-7 (Families of Functions and Absolute Value Functions) ALGEBRA II HONORS/GIFTED.

Graph Absolute Value Functions using Transformations

Absolute Value Functions

Graph Absolute Value Functions using Transformations

4.1 Quadratic Functions and Transformations

Graphs of Quadratic Functions

I can Shift, Reflect, and Stretch Graphs

Vertical Stretches and Compressions

Objectives Transform quadratic functions.

Translating Parabolas

5-7 Warm Up – Discovery with Partners

Section 2.5 Transformations.

Graph Absolute Value Functions using Transformations

2.5 Stretching, Shrinking, and Reflecting Graphs

Objectives Transform quadratic functions.

Graph Absolute Value Functions using Transformations

Lesson 5.3 Transforming Parabolas

Lesson 5-1 Graphing Absolute Value Functions

Chapter 15 Review Quadratic Functions.

Family of Quadratic Functions

Reflections and Symmetry

Shifting a Function’s Graph

Transformation of Graphs

Who Wants to Be a Transformation Millionaire?

Chapter 2: Analysis of Graphs of Functions

Chapter 15 Review Quadratic Functions.

Warm-up: Welcome Ticket

1.5b Combining Transformations

2.1 Transformations of Quadratic Functions

6.4a Transformations of Exponential Functions

Bell Ringer 1. What is the Quadratic Formula?

The vertex of the parabola is at (h, k).

1.5b Combining Transformations

I will write a quadratic function in vertex form.

Warm Up (5 Minutes) (-2,-2); Translated: Vertically 4, Horizontally -3

6.4c Transformations of Logarithmic functions

LEARNING GOALS FOR LESSON 2.6 Stretches/Compressions

15 – Transformations of Functions Calculator Required

Presentation transcript:

Quadratic Functions, Translation and Reflection Lesson 2.2

Quadratic Function Standard form Vertex form a, b, and c are constants a ≠ 0 (why?) Vertex form (h, k) is the vertex of the parabola value for a is the same in both forms

Vertex of Parabola X-value of vertex at Y-value of vertex at For

Translations In the Y= screen, enter the function Now enter the variations as shown Predict the results of the variations Set style: dotted thick

Horizontal Translations Shift to the right f(x – a) Shift to the left f(x + a)

Translations Now try … make predictions These changes created vertical translations f(x) + a shift up f(x) – a shift down

Translations What about? Predictions? When a > 1 gives vertical stretch When 0 < a < 1 gives vertical compression

Reflections Make your predictions again for these variations -f(x) gives reflection in the x-axis f(-x) gives reflection in y-axis

Combinations Given What happens when we have these variations?

Assignment Lesson 2.2 Page 79 Exercises 1 – 61 EOO