5.1 Modeling Data with Quadratic Functions. Quadratic Function: f(x) = ax 2 + bx + c a cannot = 0.

Slides:

Advertisements

Similar presentations

5.2 Properties of Parabolas

Advertisements

5.2 Properties of Parabolas

6.1/6.2/6.6/6.7 Graphing , Solving, Analyzing Parabolas

Algebra II w/ trig 4.1 Quadratic Functions and Transformations

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-

5.1 – Introduction to Quadratic Functions Objectives: Define, identify, and graph quadratic functions. Multiply linear binomials to produce a quadratic.

5.1 – Introduction to Quadratic Functions Objectives: Define, identify, and graph quadratic functions. Multiply linear binomials to produce a quadratic.

 Quadratic function ◦ A function that can be written in the standard form ◦ ax 2 +bx+c ◦ a is never “0” ◦ Domain of the function is all real numbers.

3. Graph Quadratic Functions in Standard Form 3.1 Graph Quadratic Functions in Standard Form WEDNESDAY JAN 26 TH p. 56.

5.1 Modeling Data with Quadratic Functions Quadratic function: a function that can be written in the standard form of f(x) = ax 2 + bx + c where a does.

Graphing Quadratic Equations

Properties of Quadratic Functions in Standard Form.

5-1: MODELING DATA WITH QUADRATIC FUNCTIONS Essential Question: Describe the shape of the graph of a quadratic function and basic properties of the graph.

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

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

5-1 Modeling Data With Quadratic Functions Big Idea: -Graph quadratic functions and determine maxima, minima, and zeros of function. -Demonstrate and explain.

4.1 Graph Quadratic Functions in Standard Form

Modeling Data With Quadratic Functions

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.

5.2 Graphing Quadratic Functions in Vertex Form 12/5/12.

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.

WARM UP What is the x-coordinate of the vertex? 1.y = -2x 2 + 8x – 5 2.y = x 2 + 3x -2 4.

Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing  DESCRIBE the Elements of the GRAPH of a Quadratic Equation  DETERMINE a Standard Approach.

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.

Big Idea: -Graph quadratic functions. -Demonstrate and explain the effect that changing a coefficient has on the graph. 5-2 Properties of Parabolas.

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:

4.2 Standard Form of a Quadratic Function The standard form of a quadratic function is f(x) = ax² + bx + c, where a ≠ 0. For any quadratic function f(x)

Bellwork  Identify the domain and range of the following quadratic functions

 I will be able to identify and graph quadratic functions. Algebra 2 Foundations, pg 204.

GRAPH QUADRATIC FUNCTIONS. FIND AND INTERPRET THE MAXIMUM AND MINIMUM VALUES OF A QUADRATIC FUNCTION. 5.1 Graphing Quadratic Functions.

Determine if each is a quadratic equation or not.

Do Now Find the value of y when x = -1, 0, and 2. y = x2 + 3x – 2

5-2 Properties of Parabolas

Algebra Lesson 10-2: Graph y = ax2 + bx + c

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

Section 5.1 Modeling Data with Quadratic Functions Objective: Students will be able to identify quadratic functions and graphs, and to model data with.

Algebra I Section 9.3 Graph Quadratic Functions

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

Quadratic Equations Chapter 5.

Chapter 4: Quadratic Functions and Equations

4.1 Quadratic Functions and Transformations

Characteristics of Quadratic functions

How to Graph Quadratic Equations

Graphing Quadratic Functions

How To Graph Quadratic Equations

Solving a Quadratic Equation by Graphing

KnighT’s Charge 8/26/15 A. Complete the “Victory Lap”.

Quadratic Functions Unit 9 Lesson 2.

Quadratic Functions.

5.1 Modeling Data with Quadratic Functions

CHAPTER 6 SECTION 1 GRAPHING QUADRATIC FUNCTIONS

3.1 Quadratic Functions and Models

Find the x-coordinate of the vertex

Graphing Quadratic Functions (2.1.1)

Characteristics of Quadratic functions

How To Graph Quadratic Equations.

Review: Simplify.

Some Common Functions and their Graphs – Quadratic Functions

Graphing Quadratic Functions

3.1 Quadratic Functions and Models

Graphing Quadratic Functions

How To Graph Quadratic Equations.

Section 10.2 “Graph y = ax² + bx + c”

Solving Quadratic Equations by Graphing

Quadratic Functions and Modeling

Characteristics of Quadratic functions

Determine if each is a quadratic equation or not.

Characteristics of Quadratic functions

Quadratic Functions and Equations Lesson 1: Graphing Quadratic Functions.

Presentation transcript:

5.1 Modeling Data with Quadratic Functions

Quadratic Function: f(x) = ax 2 + bx + c a cannot = 0

Ex 1 Is the function linear or quadratic? f(x) = (2x – 1) 2

EX 2 Is the function linear or quadratic? f(x) = x 2 – (x + 1)(x – 1)

The graph of a quadratic function is a PARABOLA. Vertex – minimum or maximum value. Where the parabola intersects the axis of symmetry. Axis of Symmetry – a line that divides the parabola into 2 parts, mirror images

EX 3 Find the vertex, axis of symmetry and the corresponding points to P and Q. y = x 2 – 6x + 11

EX 4 Find a quadratic function to model the given points: (-2, -17) (1, 10) (5, -10)

Ex 5 y = 2x 2 + x – c contains the point (1, 2). Find c.