Section 8.6 Quadratic Functions & Graphs  Graphing Parabolas f(x)=ax 2 f(x)=ax 2 +k f(x)=a(x–h) 2 f(x)=a(x–h) 2 +k  Finding the Vertex and Axis of Symmetry.

Slides:

Advertisements

Similar presentations

Parabolas and Modeling

Advertisements

Using Transformations to Graph Quadratic Functions 5-1

Previously, we worked with linear functions, in which the highest exponent of the variable x was 1. In this section, we find ourselves working with quadratic.

EXAMPLE 1 Graph y= ax 2 where a > 1 STEP 1 Make a table of values for y = 3x 2 x– 2– 1012 y12303 Plot the points from the table. STEP 2.

Quadraticsparabola (u-shaped graph) y = ax2 y = -ax2 Sketching Quadratic Functions A.) Opens up or down: 1.) When "a" is positive, the graph curves upwards.

And the Quadratic Equation……

Topic: U2 L1 Parts of a Quadratic Function & Graphing Quadratics y = ax 2 + bx + c EQ: Can I identify the vertex, axis of symmetry, x- and y-intercepts,

Graphing Quadratics With VERTEX and Axis of Symmetry At the end of the period, you will learn: 1. To compare parabola by the coefficient 2. To find the.

Quadratic Functions and Their Graphs

Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 1 Chapter 9 Quadratic Equations and Functions.

1.8 QUADRATIC FUNCTIONS A function f defined by a quadratic equation of the form y = ax 2 + bx + c or f(x) = ax 2 + bx + c where c  0, is a quadratic.

Graphs of Quadratic Function Introducing the concept: Transformation of the Graph of y = x 2.

10.1 Graphing Quadratic Functions p. 17. Quadratic Functions Definition: a function described by an equation of the form f(x) = ax 2 + bx + c, where a.

Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities Chapter 5 – Quadratic Functions and Inequalities 5.7 – Analyzing Graphs of Quadratic.

Holt Algebra Using Transformations to Graph Quadratic Functions Transform quadratic functions. Describe the effects of changes in the coefficients.

Section 4.1 – Quadratic Functions and Translations

6 minutes Warm-Up For each parabola, find an equation for the axis of symmetry and the coordinates of the vertex. State whether the parabola opens up.

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.

Vertex Form November 10, 2014 Page in Notes.

4.1 Quadratic Functions and Transformations A parabola is the graph of a quadratic function, which you can write in the form f(x) = ax 2 + bx + c, where.

QUADRATIC FUNCTIONS IN STANDARD FORM 4.1B. Review  A quadratic function can be written in the form y = ax 2 + bx + c.  The graph is a smooth curve called.

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.

Warm Up Lesson 4.1 Find the x-intercept and y-intercept

Objectives Transform quadratic functions.

5-1 Graphing Quadratic Functions Algebra II CP. Vocabulary Quadratic function Quadratic term Linear term Constant term Parabola Axis of symmetry Vertex.

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

1 PRECALCULUS Section 1.6 Graphical Transformations.

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.

Quadratic Graphs and Their Properties

Parabolas Objective: Understand Properties of Parabolas, Translate Parabolas, and Quadratic Functions.

How To Graph Quadratic Equations Standard Form.

Chapter 3 Quadratic Functions

Quadratic Functions and Their Graphs

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

13 Algebra 1 NOTES Unit 13.

Using Transformations to Graph Quadratic Functions 5-1

Interesting Fact of the Day

2-7 Absolute Value Functions and Graphs

Properties of Quadratic Functions in Standard Form 5-1

Objective Graph and transform quadratic functions.

Objectives Transform quadratic functions.

Chapter 5 Quadratic Functions

ALGEBRA I : SECTION 9-1 (Quadratic Graphs and Their Properties)

Objectives Transform quadratic functions.

Graphing Quadratic Equations

parabola up down vertex Graph Quadratic Equations axis of symmetry

Quadratic Functions.

CHAPTER 6 SECTION 1 GRAPHING QUADRATIC FUNCTIONS

4.1 & 4.2 Graphing Quadratic Functions

Find the x-coordinate of the vertex

Quadratic Functions and Their Graph

Review: Simplify.

Warm-up: Sketch y = 3|x – 1| – 2

Chapter 8 Quadratic Functions.

Quadratic Functions in the Form y = a(x – h)2 + k

Some Common Functions and their Graphs – Quadratic Functions

ALGEBRA II ALGEBRA II HONORS/GIFTED - SECTIONS 4-1 and 4-2 (Quadratic Functions and Transformations AND Standard and Vertex Forms) ALGEBRA.

Chapter 8 Quadratic Functions.

Before: March 19, 2018 For each quadratic function, find the axis of symmetry and vertex, and state whether the function opens upward or downward.

Copyright © 2006 Pearson Education, Inc

Graphing Quadratic Functions in Vertex form

Section 10.2 “Graph y = ax² + bx + c”

Translations & Transformations

Objective Graph and transform quadratic functions.

Graphing f(x) = (x - h) + k 3.3A 2 Chapter 3 Quadratic Functions

Section 8.1 “Graph y = ax²”.

9-3 Graphing y = ax + bx + c up 1a. y = x - 1 for -3<x<3

How To Graph Quadratic Equations.

Quadratic Functions and Equations Lesson 1: Graphing Quadratic Functions.

Presentation transcript:

Section 8.6 Quadratic Functions & Graphs  Graphing Parabolas f(x)=ax 2 f(x)=ax 2 +k f(x)=a(x–h) 2 f(x)=a(x–h) 2 +k  Finding the Vertex and Axis of Symmetry  Finding Maximums or Minimums 8.61

Definition Let’s make a table of values for f(x) = x 2 Then sketch the basic parabola shape … 8.62

Make a table of values for f(x) = x 2 Then graph it 8.63

Similar Curves  Changing the coefficient of x 2 :  Smaller is wider  Larger is narrower  The vertex remains the same 8.64

Make a table of values for f(x) = -½x 2 Then graph it 8.65

Reflections  The graph of y= -ƒ(x) is the graph of y = ƒ(x) reflected about the x-axis. 8.66

Vertical Translations If ƒ is a function and k is a positive number, then  The graph of y = ƒ(x) + k is identical to the graph of y =ƒ(x) except that it is translated k units upward.  The graph of y = ƒ(x) - k is identical to the graph of y = ƒ(x) except that it is translated k units downward.  Sketch f(x) = x on the board 8.67

Horizontal Translations If ƒ is a function and h is a positive number,  Then the graph of y = ƒ(x - h) is identical to the graph of y = ƒ(x) except that it is translated h units to the right.  The graph of y = ƒ(x + h) is identical to the graph of y = ƒ(x) except that it is translated h units to the left. 8.68

Graph f(x) = (x – 3)

Graph g(x) = -2(x +4)

8.611

Graph g(x) = (x – 3) 2 –

Finding the Vertex and Axis of Symmetry Answer the following questions about the given equation: a. Does the graph open upward or downward? b. What are the coordinates of the vertex? c. What is the axis of symmetry? d. Is it narrow or wide? Up (5,1) x=5 narrow 8.613

Finding the Vertex and Axis of Symmetry Answer the following questions about the given equation: a. Does the graph open upward or downward? b. What are the coordinates of the vertex? c. What is the axis of symmetry? d. Is it narrow or wide? Down (-4,-3) x=-4 wide 8.614

Maximums & Minimums 8.615

Maximum or Minimum? Vertex and Axis of Symmetry? 8.616

But what if the function is not in the form of f(x) = a(x – h) 2 + k ? 8.617

What Next?  Section 9.1 Section 9.1 Composite Functions  Sections may not be covered