Graphing Quadratic Functions in Standard From Section 7.2.

Slides:

Advertisements

Similar presentations

Parabola Conic section.

Advertisements

Vocabulary axis of symmetry standard form minimum value maximum value.

By: Silvio, Jacob, and Sam.  Linear Function- a function defined by f(x)=mx+b  Quadratic Function-a function defined by f(x)=ax^2 + bx+c  Parabola-

If the leading coefficient of a quadratic equation is positive, then the graph opens upward. axis of symmetry f(x) = ax2 + bx + c Positive #

Chapter 10 Quadratic Equations and Functions Section 5 Graphing Quadratic Functions Using Properties.

Quadratic Functions, Quadratic Expressions, Quadratic Equations

Section 7.5 – Graphing Quadratic Functions Using Properties.

Essential Question: How do you determine whether a quadratic function has a maximum or minimum and how do you find it?

FURTHER GRAPHING OF QUADRATIC FUNCTIONS Section 11.6.

Identify the axis of symmetry for the graph of Rewrite the function to find the value of h. h = 3, the axis of symmetry is the vertical line x = 3. Bell.

Using the Quadratic Formula to Solve Quadratic Equations Section 7.5.

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

Algebra 2 (Section 4.9).

Quadratic Functions Chapter 7. Vertex Form Vertex (h, k)

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

Goal: Graph quadratic functions in different forms.

Graphing Linear Equations Section 1.2. Lehmann, Intermediate Algebra, 3ed Section 1.2 Consider the equation. Let’s find y when So, when, which can be.

Holt McDougal Algebra Properties of Quadratic Functions in Standard Form This shows that parabolas are symmetric curves. The axis of symmetry is.

Modeling with Quadratic Functions Section 7.8. Lehmann, Intermediate Algebra, 4ed Section 7.8Slide 2 Using a Quadratic Function to Make Predictions Using.

Graphing Quadratic Functions Graph quadratic functions of the form f ( x ) = ax 2. 2.Graph quadratic functions of the form f ( x ) = ax 2 + k. 3.Graph.

Solving Polynomial Equations in Factored Form Lesson 10.4A Algebra 2.

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.

Learning Task/Big Idea: Students will learn how to find roots(x-intercepts) of a quadratic function and use the roots to graph the parabola.

Objectives Vocabulary zero of a function axis of symmetry

 Graph is a parabola.  Either has a minimum or maximum point.  That point is called a vertex.  Use transformations of previous section on x 2 and -x.

The Vertex of a Parabola Finding the Maximum or Minimum.

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

GRAPHING QUADRATIC FUNCTIONS

2.1 – Quadratic Functions.

1.The standard form of a quadratic equation is y = ax 2 + bx + c. 2.The graph of a quadratic equation is a parabola. 3.When a is positive, the graph opens.

Advanced Algebra Notes

$200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400 $600 $800 $1000 $200 $400.

Section 9.1 Quadratic Functions and Their Graphs.

Using the Quadratic Formula to Solve Quadratic Equations Section 7.5.

Objectives Define, identify, and graph quadratic functions.

6-1 Graphing Quadratic Functions

Warm - Up Graph the following transformations. Announcements Assignment ◦p. 214 ◦#12, 13, 16, 17, 20, 22, 24, Cargo Pants Legends Make Up Tests ◦After.

Working With Quadratics M 110 Modeling with Elementary Functions Section 2.1 Quadratic Functions V. J. Motto.

Finding Linear Equations Section 1.5. Lehmann, Intermediate Algebra, 4ed Section 1.5Slide 2 Using Slope and a Point to Find an Equation of a Line Find.

Holt McDougal Algebra Characteristics of Quadratic Functions Warm Up Find the x-intercept of each linear function. 1. y = 2x – y = 3x + 6.

Graphing quadratic functions part 2. X Y I y = 3x² - 6x + 2 You have to find the vertex before you can graph this function Use the formula -b 2a a = 3.

Dear Power point User, This power point will be best viewed as a slideshow. At the top of the page click on slideshow, then click from the beginning.

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:

Function Notation and Making Predictions Section 2.3.

Unit 10 – Quadratic Functions Topic: Characteristics of Quadratic Functions.

Warm-up: 1. Graph y = -4x – 3 2. Find f(3) when f(x) = 3x + 2.

Key Components for Graphing a Quadratic Function.

Solving Quadratic Equations Graphically Math 2 Spring 2016 Mrs. Brown.

Determine if each is a quadratic equation or not.

5-2 Properties of Parabolas

Quadratic Functions, Quadratic Expressions, Quadratic Equations

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

Warm Up /31/17 1. Evaluate x2 + 5x for x = 4 and x = –3. __; ___

Quadratic Functions and Their Properties

Notes 3.3 Quadratic Functions

Graphing Quadratic Functions in Standard From

Graphing Quadratics in Standard Form

THE VERTEX OF A PARABOLA

Quadratic Functions.

Quadratic Functions and Their Graph

Objectives Find the zeros of a quadratic function from its graph.

Graphing Quadratic Equations

Algebra 2 – Chapter 6 Review

Quadratic Functions and Their Properties

Notes Over 5.8 Writing a Quadratic Function in Vertex Form

Determine if each is a quadratic equation or not.

QUADRATIC FUNCTION Given a Function y = 2x2 -6x -8 in domain

Presentation transcript:

Graphing Quadratic Functions in Standard From Section 7.2

Lehmann, Intermediate Algebra, 4ed Section 7.2Slide 2 Method 2: Graphing by Using the Vertex Formula to Find the Vertex Vertex Formula To find the vertex of the graph of a quadratic function 1.Find the x-coordinate of the vertex by using the vertex formula 2. Find the y-coordinate of the vertex by evaluating f at the value found in step 1. That is, find − b 2a. Process

Lehmann, Intermediate Algebra, 4ed Find the vertex of the graph of a = 1, b = –4, and c = 7 Find the x-coordinate by substituting a and b into the formula Find the y-coordinate by finding f (2): So, the vertex is (2, 3) Section 7.2Slide 3 Method 2: Graphing by Using the Vertex Formula to Find the Vertex Using the Vertex Formula to Find the Vertex Example Solution

Lehmann, Intermediate Algebra, 4ed Section 7.2Slide 4 Method 2: Graphing by Using the Vertex Formula to Find the Vertex Using the Vertex Formula to Graph a Quadratic Function Sketch a graph of a = 2, b = 10, and c = 7 Find the x-coordinate of the vertex: Find the y-coordinate of the vertex: So, the vertex is (–2.5, –5.5) Find additional input-output pairs: Example Solution

Lehmann, Intermediate Algebra, 4ed Section 7.2Slide 5 Method 2: Graphing by Using the Vertex Formula to Find the Vertex Using the Vertex Formula to Graph a Quadratic Function ExampleSolution Continued

Lehmann, Intermediate Algebra, 4ed Section 7.2Slide 6 Method 2: Graphing by Using the Vertex Formula to Find the Vertex Using the Vertex Formula to Graph a Quadratic Function Sketch a graph of a = –2.2, b = 6.1, and c = 1.4 Find the x-coordinate of the vertex: Find the y-coordinate of the vertex: So, the vertex is (1.39, 5.63) Find additional input-output pairs: Example Solution

Lehmann, Intermediate Algebra, 4ed Section 7.2Slide 7 Method 2: Graphing by Using the Vertex Formula to Find the Vertex Using the Vertex Formula to Graph a Quadratic Function ExampleSolution Continued

Lehmann, Intermediate Algebra, 4ed Section 7.2Slide 8 Minimum of Maximum Value Maximum of Minimum Value of a Function For a quadratic function whose graph has vertex (h, k), If a < 0, then the parabola opens downward and the maximum value of the function is k If a > 0, then the parabola opens upward and the minimum value of the function is k Property