Warm Up Graph: 1.y > 2x + 3 2.y < 1/3x – 2. M2 3.9 (M2) Graph & Solve Quadratic Inequalities Performance Exam: THURSDAY! Computer Lab: Friday Last Unit.

Slides:

Advertisements

Similar presentations

5.7 Quadratic Inequalities

Advertisements

Linear Inequalities in 2 Variables

4.6 (M2) Solve Exponential Equations and Inequalities Performance Exam: Dec. 2 Last Unit Test: Dec. 8 EOCT: Dec. 16 (6 th ), Dec. 17 (7 th ) We will go.

7-5 solving quadratic equations

2-7 Solving quadratic inequalities

5.7 : Graphing and Solving Quadratic Inequalities

Adapted from Walch Education  Quadratic inequalities can be written in the form ax 2 + bx + c < 0, ax 2 + bx + c ≤ 0, ax 2 + bx + c > 0, or ax 2 + bx.

School starts at 7:15 for EOCT testing!

Objective Graph and solve systems of linear inequalities in two variables.

5.8 Quadratic Inequalities

Table of Contents Graphing Systems of Linear Inequalities It is assumed you already know how to graph a linear inequality, which was discussed in a previous.

Systems of Linear Inequalities.  Two or more linear inequalities together form a system of linear inequalities.

Solve Systems of Equations By Graphing

3.4 Solving Systems of Linear Inequalities Objectives: Write and graph a system of linear inequalities in two variables. Write a system of inequalities.

1. Graph the inequality y < 2x + 1.

8.8 Linear Inequalities, Systems, and Linear Programming.

Warm Up 1. Graph the inequality y < 2x + 1. Solve using any method. 2. x 2 – 16x + 63 = x 2 + 8x = 3 7, 9.

Unit 2 – Quadratic, Polynomial, and Radical Equations and Inequalities Chapter 5 – Quadratic Functions and Inequalities 5.8 – Graphing and Solving Quadratic.

Set Operations and Compound Inequalities. 1. Use A = {2, 3, 4, 5, 6}, B = {1, 3, 5, 7, 9}, and C = {2, 4, 6, 8} to find each set.

Solving Linear Inequalities `. Warm-up -4 < x ≤ 6 x ≤ -4 or x>

1. Graph the inequality y < 2x + 1.

Section 4.7 – The Quadratic Formula Students will be able to: To solve equations using the Quadratic Formula To determine the number of solutions by using.

4.9 – Graph and Solve Quadratic Inequalities A quadratic inequality in two variables can be written in one of the following forms: y < ax 2 + bx + c y.

WARM UP EVALUATING EXPRESSIONS Evaluate the expression for the given value of the variable (Lesson 2.5). 1.-3(x) when x = 9 2.4(-6)(m) when m = (-n)(-n)

WARM UP Find the product. 1.) (m – 8)(m – 9) 2.) (z + 6)(z – 10) 3.) (y + 20)(y – 20)

Graphing & Solving Quadratic Inequalities 5.7 What is different in the graphing process of an equality and an inequality? How can you check the x-intercepts.

EXAMPLE 1 Solve an equation with two real solutions Solve x 2 + 3x = 2. x 2 + 3x = 2 Write original equation. x 2 + 3x – 2 = 0 Write in standard form.

Holt McDougal Algebra Solving Quadratic Inequalities 2-7 Solving Quadratic Inequalities Holt Algebra 2 Warm Up Warm Up Lesson Presentation Lesson.

M3 1.5 Systems of Linear Inequalities M3 1.5 Systems of Linear Inequalities Essential Questions: How can we write and graph a system of linear inequalities.

-What is quadratic inequality -How to graph quadratic inequality 4-8 Quadratic Inequalities.

Solving Quadratic Equations by Factoring. The quadratic equation is written in the form ax 2 + bx + c = 0 To solve quadratic equations by factoring we.

Algebra 2 9/22/14 Bellwork:. 2.8 – Graph Linear Inequalities in Two Variables A linear inequality in two variables can be written in one of these forms:

Warm Up 1.) What is the graph of the function y = -x 2 + 4x + 1?

Holt McDougal Algebra Solving Quadratic Inequalities Solve quadratic inequalities by using tables and graphs. Solve quadratic inequalities by using.

Aim: How do we graph and solve quadratic inequality in two variables? Do Now: Graph y < x – 4.

Table of Contents First, write the inequality in the formax 2 + bx + c > 0. Quadratic Inequality: Solving Algebraically EXAMPLE: Solve 3x 2  7x > 6. 3x.

ALGEBRA TWO CHAPTER FIVE QUADRATIC FUNCTIONS SECTION SEVEN Graphs of Quadratic Inequalities.

Holt McDougal Algebra Solving Systems of Linear Inequalities Solve systems of linear inequalities. Objective.

Notes Over 1.6 Solving an Inequality with a Variable on One Side Solve the inequality. Then graph your solution. l l l

Review: Algebra. Write numeric expressions:  Numeric expressions are expressions written out as phrases  Example:  Written as: The difference.

Algebra 1 Section 7.6 Solve systems of linear inequalities The solution to a system of linear inequalities in two variable is a set of ordered pairs making.

Graphing and Solving Quadratic Inequalities CHAPTER 5 LESSON 8.

4.9: Graph and Solve Quadratic Inequalities Objectives: Solve quadratic inequalities by using tables and graphs. Solve quadratic inequalities by using.

Aim: How do we solve quadratic inequalities? Do Now: Solve and graph 1) 8|-2x| - 2 > 30 2) -4|-3 + 7x| + 9 ≥ -59 HW #5 – Handout #2,6,12,16,21 (solve and.

Algebra 1 Section 6.5 Graph linear inequalities in two variables.

Graphing a System of Inequalities

Chapter 9 Linear and Quadratic Inequalities

Quadratic Inequalities

Warm Up Solve each inequality for y. 1. 8x + y < 6

6-7 Graphing and Solving Quadratic Inequalities

Use back - substitution to solve the triangular system. {image}

The Quadratic Formula.

Warm Up Graph y = 4x and 16, $10’s and 7 $20’s.

Objective Solve quadratic equations by graphing.

Linear Inequalities in Two Variables

Solving Systems of 5-6 Linear Inequalities Warm Up Lesson Presentation

Solving Quadratic Inequalities

Solve Systems of Linear Inequalities

WARM UP 3 EVALUATING RADICAL EXPRESSIONS Evaluate the radical expression when a = -1 and b = 5. (LESSON 9.1). b 2 − 11a b 2 +9a a 2 +8.

Algebra 2 10/19/16 EQ: How do I complete the square to solve for x

7.6 Graphing Systems of Linear Inequalities

Warm Up Graph y = 4x and 16, $10’s and 7 $20’s.

Algebra 1B – Name: _________________________

4.9 Notes – Graph and Solve Quadratic Inequalities

Warm Up #4 1. Write 15x2 + 6x = 14x2 – 12 in standard form. ANSWER

3-3 Systems of Inequality

L1-4 Algebra 2.

Warm Up 1. Graph y = x2 + 4x Identify the vertex and zeros of the function above. vertex:(–2 , –1); zeros:–3, –1.

Section 9.4 Graphing Linear Inequalities in Two Variables and Systems of Linear Inequalities.

Warm up – Solve the Quadratic

Presentation transcript:

Warm Up Graph: 1.y > 2x y < 1/3x – 2

M2 3.9 (M2) Graph & Solve Quadratic Inequalities Performance Exam: THURSDAY! Computer Lab: Friday Last Unit Test: Dec. 8 EOCT: Dec. 17

Vocabulary A quadratic inequality in two variables can be written in one of the following forms: y < ax² + bx + c y ≤ ax² + bx + c y > ax² + bx + c y ≥ ax² + bx + c

Vocabulary A quadratic inequality in one variable can be written in one of the following forms: ax² + bx + c < 0 ax² + bx + c ≤ 0 ax² + bx + c > 0 ax² + bx + c ≥ 0

Example 1: Graph the system y < -x² - x + 2 y ≥ x² - 2x – 2

Step 3: Identify the shaded region where the two graphs overlap. It is the graph of the system.

Example 2 Example 2 – Solve a quadratic inequality Solve x² - 5x ≤ - 4 a)Using a table Rewrite as x² - 5x + 4 ≤ 0 and make a table of values. x x² - 5x + 4

The solution of the inequality is 1 ≤ x ≤ 4. b) Solve x² - 5x ≤ - 4 by graphing,

The solution of the inequality is 1 ≤ x ≤ 4.

c) Solve x² - 5x ≤ - 4 algebraically. First replace ≤ with =. x² - 5x = - 4 x² - 5x + 4 = 0 Factor. (x – 4)(x – 1) = 0 x = 4, 1 lessAND: 1 < x < 4

Classwork/Homework P #1-15odd, 28-33