Warm Up Graph: 1.y > 2x + 3 2.y < 1/3x – 2. M2 3.9 (M2) Graph & Solve Quadratic Inequalities...
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Transcript of Warm Up Graph: 1.y > 2x + 3 2.y < 1/3x – 2. M2 3.9 (M2) Graph & Solve Quadratic Inequalities...
![Page 1: 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.](https://reader035.fdocuments.in/reader035/viewer/2022072015/56649ec55503460f94bd0356/html5/thumbnails/1.jpg)
Warm Up
Graph: 1. y > 2x + 3
2. y < 1/3x – 2
![Page 2: 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.](https://reader035.fdocuments.in/reader035/viewer/2022072015/56649ec55503460f94bd0356/html5/thumbnails/2.jpg)
3.9 (M2M2) Graph & Solve Quadratic
Inequalities
Performance Exam: THURSDAY!
Computer Lab: Friday
Last Unit Test: Dec. 8
EOCT: Dec. 17
![Page 3: 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.](https://reader035.fdocuments.in/reader035/viewer/2022072015/56649ec55503460f94bd0356/html5/thumbnails/3.jpg)
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
![Page 4: 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.](https://reader035.fdocuments.in/reader035/viewer/2022072015/56649ec55503460f94bd0356/html5/thumbnails/4.jpg)
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
![Page 5: 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.](https://reader035.fdocuments.in/reader035/viewer/2022072015/56649ec55503460f94bd0356/html5/thumbnails/5.jpg)
Example 1:Example 1:
Graph the system
• y < -x² - x + 2
• y ≥ x² - 2x – 2
![Page 6: 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.](https://reader035.fdocuments.in/reader035/viewer/2022072015/56649ec55503460f94bd0356/html5/thumbnails/6.jpg)
Step 3: Identify the shaded region where the two graphs overlap. It is the graph of the system.
![Page 7: 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.](https://reader035.fdocuments.in/reader035/viewer/2022072015/56649ec55503460f94bd0356/html5/thumbnails/7.jpg)
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
![Page 8: 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.](https://reader035.fdocuments.in/reader035/viewer/2022072015/56649ec55503460f94bd0356/html5/thumbnails/8.jpg)
• The solution of the inequality is
1 ≤ x ≤ 4.
b) Solve x² - 5x ≤ - 4 by graphing,
![Page 9: 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.](https://reader035.fdocuments.in/reader035/viewer/2022072015/56649ec55503460f94bd0356/html5/thumbnails/9.jpg)
• The solution of the inequality is
1 ≤ x ≤ 4.
![Page 10: 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.](https://reader035.fdocuments.in/reader035/viewer/2022072015/56649ec55503460f94bd0356/html5/thumbnails/10.jpg)
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
![Page 11: 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.](https://reader035.fdocuments.in/reader035/viewer/2022072015/56649ec55503460f94bd0356/html5/thumbnails/11.jpg)
Classwork/Homework
• P. 98-99 #1-15odd, 28-33