9.5 Solving Quadratic Equations by Graphing Ms. Wu.

Slides:

Advertisements

Similar presentations

Warm-Up: December 15, 2011  Divide and express the result in standard form.

Advertisements

Solving Quadratic Equations by Graphing

Warm-Up: you should be able to answer the following without the use of a calculator 2) Graph the following function and state the domain, range and axis.

Anatomy of a Quadratic Function. Quadratic Form Any function that can be written in the form Ax 2 +Bx+C where a is not equal to zero. You have already.

Quadratic Functions & Inequalities

HW#1: Two Problems on graph paper

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.

Identifying Key Features of Graphs of Quadratic Functions

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

Quiz review Direction of Opening Y – intercept Vertex AOS

Monday, 4/30Tuesday, 5/1Wednesday, 5/2Thursday, 5/3Friday, 5/4 No classes Review for tomorrow’s test TEST!Quadratic graphs Quadratic Graphs Monday, 5/7Tuesday,

Warm-Up Find the vertex, the roots or the y- intercept of the following forms: 1. f(x) = (x-4) f(x) = -2(x-3)(x+4) 3. f(x) = x 2 -2x -15 Answers:

Warmup 9-11 Solve the following equations by factoring. Show work! 1.x x - 80 = 0 2.Solve by using the quadratic formula: 4x 2 - 5x - 2 = 0 3.Solve.

Algebra 1B Chapter 9 Solving Quadratic Equations By Graphing.

Definitions 4/23/2017 Quadratic Equation in standard form is viewed as, ax2 + bx + c = 0, where a ≠ 0 Parabola is a u-shaped graph.

Quadratic Vocabulary Words to graph by….

1 Warm-up Factor the following x 3 – 3x 2 – 28x 3x 2 – x – 4 16x 4 – 9y 2 x 3 + x 2 – 9x - 9.

Graphing Quadratic Equations Standard Form & Vertex Form.

Properties of Quadratic Functions in Standard Form.

Characteristics of Quadratics

Warm ups – I will stamp hw tomorrow! Factor Solve.

4.1 Notes – Graph Quadratic Functions in Standard Form.

10.1 & 10.2: Exploring Quadratic Graphs and Functions Objective: To graph quadratic functions.

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

Solving Quadratic Equations by Graphing 4 Lesson 10.2.

Direction: _____________ Width: ______________ AOS: _________________ Set of corresponding points: _______________ Vertex: _______________ Max or Min?

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.

SWBAT…analyze the characteristics of the graphs of quadratic functions Wed, 2/15 Agenda 1. WU (10 min) 2. Characteristics of quadratic equations (35 min)

Complete the table and graph x (x - 3) Vertex.

Solve:. Need Help? Look in textbook in Section 5.1: Modeling Data w/ Quadratic Functions Section 5.2: Properties of Parabolas Worksheet: Properties of.

Vocabulary of a Quadratic Function Vacation… November 30, 2015.

Graphs of Quadratics Let’s start by graphing the parent quadratic function y = x 2.

 Standard Form  y = ax 2 + bx + c, where a ≠ 0  Examples › y = 3x 2 › y = x › y = x 2 – x – 2 › y = - x 2 + 2x - 4.

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

Quadratic Functions Solving by Graphing Quadratic Function Standard Form: f(x) = ax 2 + bx + c.

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

CHAPTER 10 LESSON OBJECTIVES. Objectives 10.1 Students will be able to: Identify quadratic functions and determine whether they have a minimum or maximum.

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

Warm Up for Lesson 3.5 1)Solve: x 2 – 8x – 20 = 0 2) Sketch the graph of the equation y = 2x – 4.

9.1 Graphing Quadratic Functions. Quadratic Function A function of the form y=ax 2 +bx+c where a≠0 making a u-shaped graph called a parabola. A function.

Bellwork Find each product. 1. (x+2)(x+9) 2. (5+x)(7-4x) Solve the inequality: 3.

Graphing Quadratic Functions. The graph of any Quadratic Function is a Parabola To graph a quadratic Function always find the following: y-intercept.

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

Chapter 5 Lesson 1 Graphing Quadratic Functions Vocabulary Quadratic Function- A function described by f(x)=ax 2 +bx+c where a≠0 Quadratic Term- ax 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.

IDENTIFYING CHARACTERISTICS OF QUADRATIC FUNCTIONS A quadratic function is a nonlinear function that can be written in the standard form y = ax 2 + bx.

Quadratic Functions Sections Quadratic Functions: 8.1 A quadratic function is a function that can be written in standard form: y = ax 2 + bx.

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.

CCA WK 24 Review. Vertex Form to Standard Form y = 3(x – 3) Multiply the binomial: 3(x – 3)(x – 3) + 5 3(x 2 – 6x + 9) + 5 Distribute the “a”: 3*x.

Solving Quadratic Equations by Graphing  Quadratic Equation- A quadratic function set equal to a value, in the form ax 2 +bx+c, where a≠0  Standard.

Lesson 27 Connecting the parabola with the quadratic function.

Factor each polynomial.

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

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 Equations Chapter 5.

Mrs. Rivas Ch 4 Test Review 1.

Solving Quadratic Equation and Graphing

Y Label each of the components of the parabola A: ________________ B: ________________ C: ________________ C B B 1 2.

Graph Quadratic Functions in Standard Form

What are the equations of the following lines?

9.1 Graphing Quadratic Functions

Quadratic Functions The graph of a quadratic function is called a parabola. The parent function is given as This is the parent graph of all quadratic functions.

12.4 Quadratic Functions Goal: Graph Quadratic functions

Graphs of Quadratic Functions Part 1

4.1 Notes – Graph Quadratic Functions in Standard Form

Solve Quadratics by Graphing ax2 +bx + c

10.1: Quadratic Equations and Functions

Presentation transcript:

9.5 Solving Quadratic Equations by Graphing Ms. Wu

Warm-Up

Objectives Warm-Up (5 min.) Reminder 101 (3 min.) Review (10 min.) Quiz, Evaluation, Folder Organization ( 27 min.) Introduction (5 min.) 9.5 Workshop (20 min.) In-Class Assignment (20 min.)

Remind 101 – 3rd

Remind 101 – 4 th

Review Vertex (2, -1) y-int (0, 3) Axis of Symmetry x = 2 Domain: all real numbers Range: y ≥ -1 Minimum Opens UP Zeros: 1 and 3

Review For the parent function, y = x 2, what is the transformed function that is ____________? 7 units up: y = x times wider: y = ½x 2 1/3 times narrower and down 1 unit: y = 3x 2 – 1

Review For the function, y = x 2 +2x-1, what is the ________? Axis of symmetry? x = Vertex: (-1, -2) Does it open up or down? UP Is it a maximum or minimum? MINIMUM y-intercept: (0, -1) Domain: all real numbers Range: y ≥ -1

Quiz -> Evaluation - > Organization -> Lunch Notes Roller Coaster 1 st Blueprint 2 nd Blueprint Homework In-Class Assignments 9.2 Exploration (Axis of Symmetry) 9.4 Transformers Exploration Is your folder ready for an organization grade?? Everything must be completed…folders will be picked up for a grade next class period!!

Announcement Go to Ms. Wu’s website: annwustudentteaching.webs.comannwustudentteaching.webs.com Go to the tab “For Students (3 rd & 7 th )” New Format: Homework: Watch videos, take notes In-Class: Work on assignment, get help, quiz

Solving Quadratic Equations by Graphing A quadratic function is a function that can be written in the standard form y = ax 2 +bx+c. A quadratic equation is an equation that can be written in the standard form 0 = ax 2 +bx+c. When writing a quadratic function as its related quadratic equation you replace y with 0. Then, you solve the equation by finding its zero(s) or roots or x-int.

Ms. Wu’s hint: Remember to move everything to one side until you have everything equal to 0! Examples: 1. x 2 -8x-16=2x 2 -x 2 -8x-16 = 0 zero: x+10=-x 2 x 2 +6x+10=0 zero: none 3. –x 2 +4 = 0 zeros: -2, 2

Parabolic Solar Ovens Video: Parabolic Solar Ovens in Coast RicaParabolic Solar Ovens Video: How to Cook Food Using Solar OvensHow to Cook Food Using Solar Ovens

Joseph is trying to build a solar oven in his backyard to cut down on the cost of electricity. He did some research and found that the sun’s rays are best captured by the quadratic function y = x 2 -8x+12. Question: Joseph needs to buy a parabolic mirror at Lowe’s, how wide should the diameter of the mirror be?

Mirror needs to be 4 feet in diameter.

In-Class & Homework Complete the evens on 9-5. Turn in by the end of class. Homework: complete notes on how to FOIL and FACTOR. Watch videos online. Organize folder!!