Warm Up

Graph: 1. y > 2x + 3

2. y < 1/3x – 2

3.9 (M2M2) Graph & Solve Quadratic

Inequalities

Performance Exam: THURSDAY!

Computer Lab: Friday

Last Unit Test: Dec. 8

EOCT: Dec. 17

VocabularyVocabulary

• 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

VocabularyVocabulary

• 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: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 2Example 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 0 1 2 3 4 5

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. 98-99 #1-15odd, 28-33