1 Solving Quadratic Equations 1Shaw 2008 February 16, 2010.

Slides:

Advertisements

Similar presentations

Vocabulary axis of symmetry standard form minimum value maximum value.

Advertisements

7-5 solving quadratic equations

12-4 Quadratic Functions CA Standards 21.0 and 22.0 CA Standards 21.0 and 22.0 Graph quadratic functions; know that their roots are the x-intercepts; use.

Solving Quadratic Equations by Graphing

Table of Contents Graphing Quadratic Functions – Concept A simple quadratic function is given by The graph of a quadratic function in called a parabola.

Chapter 4 Section 4-1 Solving Quadratic Equations in Calculator.

Algebra 2 Honors Quadratic Functions.

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.

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

Topics: Standard and Vertex form of a Quadratic Function Finding Key Features of a Quadratic algebraically and graphically. Graphing Quadratics.

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.

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.

Graphing Quadratic Equations

Solving Quadratic Equations

 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.

What information can we visually determine from this Quadratic Graph? Vertex Vertical Stretch Factor (4, -3) Over 1, up 1 Over 2, up 4 Normal Pattern.

THE SLIDES ARE TIMED! KEEP WORKING! YOUR WORK IS YOUR OWN! Quadratic Systems Activity You completed one in class… complete two more for homework.

Chapter 9.1 Notes. Quadratic Function – An equation of the form ax 2 + bx + c, where a is not equal to 0. Parabola – The graph of a quadratic function.

Sec 7: Finding the Max/Min of a Quadratic Equation Learning Target: I will calculate the maximum or minimum of a quadratic equation and apply it to real-world.

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

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

11-2 Solving Quadratic Equations By Graphing

Section 5-4(e) Solving quadratic equations by factoring and graphing.

$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.

Algebra 2 Notes (9-4) Graphs of Quadratic Functions.

Chapter 5.2/Day 3 Solving Quadratic Functions by Graphing Target Goal: 1. Solve quadratic equations by graphing.

Fri 12/11 Lesson 4 – 1 Learning Objective: To graph quadratic functions Hw: Graphing Parabolas Day 1 WS.

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

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

Warm Up Find the distance between the points 1. (3,4)(6,7) 2. (-3,7)(-7,3)

Do Now: Solve the equation in the complex number system.

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:

Warm – up #7  Closed x = –2  Open x = –2 xy –2 –3 – –2 –

Interpreting Various Forms of Quadratic Equations (2.1.2) October 2nd, 2015.

Do Now: Solve the equation in the complex number system.

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

Standard Form y=ax 2 + bx + c Factor (if possible) Opening (up/down) Minimum Maximum Quadratic Equation Name________________________Date ____________ QUADRATIC.

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.

Chapter 4: Polynomials Quadratic Functions (Section 4.1)

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

Key Components for Graphing a Quadratic Function.

Notes Over 9.4 Checking a Solution Using a Graph The solution, or roots of an equation are the x-intercepts. Solve the equation algebraically. Check the.

Graphing and Solving Quadratic Inequalities CHAPTER 5 LESSON 8.

February 6, 2012 At the end of today, you will be able to solve quadratic equations by factoring. Warm-up: Factor 1.x 2 – 11x 2. x 2 – 6x – x 2.

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

Solving Quadratic Equations by Graphing Need Graph Paper!!! Objective: 1)To write functions in quadratic form 2)To graph quadratic functions 3)To solve.

Determine if each is a quadratic equation or not.

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

Quadratic Equations Chapter 5.

6.2 Solving Quadratic Equations by Graphing

Solving Quadratic Equation and Graphing

Properties of Quadratic Functions in Standard Form 5-1

Quadratic Functions Extreme Values and Graphs

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

Quadratic Functions.

Graph Quadratic Functions in Standard Form

lesson 9.1 I CAN identify parts of a parabola.

Warm Up Let’s find the vertex of the following quadratic equation and state whether it is a maximum point or minimum point.

Quadratic Functions and Their Graph

Review: Simplify.

Graphing Quadratic Functions

Obj: graph parabolas in two forms

I will write a quadratic function in vertex form.

Algebra 2 – Chapter 6 Review

Bell Work Draw a smile Draw a frown Draw something symmetrical.

Quadratic Equation Day 4

Determine if each is a quadratic equation or not.

Presentation transcript:

1 Solving Quadratic Equations 1Shaw 2008 February 16, 2010

22Shaw 2008

3 STANDARD FORM: QUADRATIC EQUATION Parabola: The graph of a Quadratic Equation 3Shaw 2008

4 Negative value for a: The Parabola opens DOWN  For example  What is the value for a? It’s a sad graph 4Shaw 2008

5 Positive value for a: The Parabola opens UP  For example  What is the value for a? It’s a happy graph! 5Shaw 2008

6 VERTEX Where would the Vertex be on these two graphs? 6Shaw 2008

7 VERTEX If a is positive: the vertex is the MINIMUM value of the function. If a is negative: the vertex is the MAXIMUM value of the function.  The Vertex always lies on the LINE OF SYMMETRY Shaw 2008

8 EXAMPLE 1 What do we know:  Does this graph open up or down?  Does the vertex have a MAXIMUM or a MINIMUM value? 8Shaw 2008

9 EXAMPLE 2  Does the graph face up or down?  Is the vertex a Max or Min? Shaw 2008

Solving Quadratic Equations When you are “solving” a quadratic equation you are finding the x-intercepts of the graph How many solutions will the equation have? Solve the following equation by graphing:

Solving Quadratic Equations Solve the following two equations algebraically What variable should we solve for?

Solving Quadratic Equations Solve the following equations algebraically

13 HOMEWORK # 14!!! Solving Quadratic Equations Worksheet #3-21 multiples of 3 #52, 53, 55 #24-45 multiples of 3, 44, 47 Shaw 2008