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Holt McDougal Algebra 2 2-7 Solving Quadratic Inequalities Warm Up 1. Graph the inequality y < 2x +...
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Transcript of Holt McDougal Algebra 2 2-7 Solving Quadratic Inequalities Warm Up 1. Graph the inequality y < 2x +...
![Page 1: Holt McDougal Algebra 2 2-7 Solving Quadratic Inequalities Warm Up 1. Graph the inequality y < 2x + 1. Solve using any method. 2. x 2 – 16x + 63 = 0 3.](https://reader036.fdocuments.net/reader036/viewer/2022083006/56649f325503460f94c4dd2e/html5/thumbnails/1.jpg)
Holt McDougal Algebra 2
2-7 Solving Quadratic Inequalities
Warm Up1. Graph the inequality y < 2x + 1.
Solve using any method.2. x2 – 16x + 63 = 0
3. 3x2 + 8x = 3
![Page 2: Holt McDougal Algebra 2 2-7 Solving Quadratic Inequalities Warm Up 1. Graph the inequality y < 2x + 1. Solve using any method. 2. x 2 – 16x + 63 = 0 3.](https://reader036.fdocuments.net/reader036/viewer/2022083006/56649f325503460f94c4dd2e/html5/thumbnails/2.jpg)
Holt McDougal Algebra 2
2-7 Solving Quadratic Inequalities
Solve quadratic inequalities by using tables and graphs.
Solve quadratic inequalities by using algebra.
Objectives
Vocabularyquadratic inequality in two variables
![Page 3: Holt McDougal Algebra 2 2-7 Solving Quadratic Inequalities Warm Up 1. Graph the inequality y < 2x + 1. Solve using any method. 2. x 2 – 16x + 63 = 0 3.](https://reader036.fdocuments.net/reader036/viewer/2022083006/56649f325503460f94c4dd2e/html5/thumbnails/3.jpg)
Holt McDougal Algebra 2
2-7 Solving Quadratic Inequalities
y < ax2 + bx + c y > ax2 + bx + c
y ≤ ax2 + bx + c y ≥ ax2 + bx + c
A quadratic inequality in two variables can be written in one of the following forms, where a, b, and c are real numbers and a ≠ 0. Its solution set is a set of ordered pairs (x, y).
![Page 4: Holt McDougal Algebra 2 2-7 Solving Quadratic Inequalities Warm Up 1. Graph the inequality y < 2x + 1. Solve using any method. 2. x 2 – 16x + 63 = 0 3.](https://reader036.fdocuments.net/reader036/viewer/2022083006/56649f325503460f94c4dd2e/html5/thumbnails/4.jpg)
Holt McDougal Algebra 2
2-7 Solving Quadratic Inequalities
Graph y ≥ x2 – 7x + 10.
Example 1: Graphing Quadratic Inequalities in Two Variables
![Page 5: Holt McDougal Algebra 2 2-7 Solving Quadratic Inequalities Warm Up 1. Graph the inequality y < 2x + 1. Solve using any method. 2. x 2 – 16x + 63 = 0 3.](https://reader036.fdocuments.net/reader036/viewer/2022083006/56649f325503460f94c4dd2e/html5/thumbnails/5.jpg)
Holt McDougal Algebra 2
2-7 Solving Quadratic Inequalities
Quadratic inequalities in one variable, such as ax2 + bx + c > 0 (a ≠ 0), have solutions in one variable that are graphed on a number line.
For and statements, both of the conditions must be true. For or statements, at least one of the conditions must be true.
Reading Math
![Page 6: Holt McDougal Algebra 2 2-7 Solving Quadratic Inequalities Warm Up 1. Graph the inequality y < 2x + 1. Solve using any method. 2. x 2 – 16x + 63 = 0 3.](https://reader036.fdocuments.net/reader036/viewer/2022083006/56649f325503460f94c4dd2e/html5/thumbnails/6.jpg)
Holt McDougal Algebra 2
2-7 Solving Quadratic Inequalities
Solve the inequality by using tables or graphs.
Example 2A: Solving Quadratic Inequalities by Using Tables and Graphs
x2 + 8x + 20 ≥ 5
Use a graphing calculator to graph each side of the inequality. Set Y1 equal to x2 + 8x + 20 and Y2 equal to 5. Identify the values of x for which Y1 ≥ Y2.
![Page 7: Holt McDougal Algebra 2 2-7 Solving Quadratic Inequalities Warm Up 1. Graph the inequality y < 2x + 1. Solve using any method. 2. x 2 – 16x + 63 = 0 3.](https://reader036.fdocuments.net/reader036/viewer/2022083006/56649f325503460f94c4dd2e/html5/thumbnails/7.jpg)
Holt McDougal Algebra 2
2-7 Solving Quadratic Inequalities
Example 2A Continued
The parabola is at or above the line when x is less than or equal to –5 or greater than or equal to –3. So, the solution set is x ≤ –5 or x ≥ –3 or (–∞, –5] U [–3, ∞). The table supports your answer.
–6 –4 –2 0 2 4 6
The number line shows the solution set.
![Page 8: Holt McDougal Algebra 2 2-7 Solving Quadratic Inequalities Warm Up 1. Graph the inequality y < 2x + 1. Solve using any method. 2. x 2 – 16x + 63 = 0 3.](https://reader036.fdocuments.net/reader036/viewer/2022083006/56649f325503460f94c4dd2e/html5/thumbnails/8.jpg)
Holt McDougal Algebra 2
2-7 Solving Quadratic Inequalities
Solve the inequality by using tables and graph.
Example 2B: Solving Quadratics Inequalities by Using Tables and Graphs
x2 + 8x + 20 < 5
![Page 9: Holt McDougal Algebra 2 2-7 Solving Quadratic Inequalities Warm Up 1. Graph the inequality y < 2x + 1. Solve using any method. 2. x 2 – 16x + 63 = 0 3.](https://reader036.fdocuments.net/reader036/viewer/2022083006/56649f325503460f94c4dd2e/html5/thumbnails/9.jpg)
Holt McDougal Algebra 2
2-7 Solving Quadratic Inequalities
The number lines showing the solution sets in Example 2 are divided into three distinct regions by the points –5 and –3. These points are called critical values. By finding the critical values, you can solve quadratic inequalities algebraically.
![Page 10: Holt McDougal Algebra 2 2-7 Solving Quadratic Inequalities Warm Up 1. Graph the inequality y < 2x + 1. Solve using any method. 2. x 2 – 16x + 63 = 0 3.](https://reader036.fdocuments.net/reader036/viewer/2022083006/56649f325503460f94c4dd2e/html5/thumbnails/10.jpg)
Holt McDougal Algebra 2
2-7 Solving Quadratic Inequalities
Solve the inequality x2 – 10x + 18 ≤ –3 by using algebra.
Example 3: Solving Quadratic Equations by Using Algebra
![Page 11: Holt McDougal Algebra 2 2-7 Solving Quadratic Inequalities Warm Up 1. Graph the inequality y < 2x + 1. Solve using any method. 2. x 2 – 16x + 63 = 0 3.](https://reader036.fdocuments.net/reader036/viewer/2022083006/56649f325503460f94c4dd2e/html5/thumbnails/11.jpg)
Holt McDougal Algebra 2
2-7 Solving Quadratic Inequalities
Example 3 Continued
Step 3 Test an x-value in each interval.
x2 – 10x + 18 ≤ –3–3 –2 –1 0 1 2 3 4 5 6 7 8 9
Critical values
![Page 12: Holt McDougal Algebra 2 2-7 Solving Quadratic Inequalities Warm Up 1. Graph the inequality y < 2x + 1. Solve using any method. 2. x 2 – 16x + 63 = 0 3.](https://reader036.fdocuments.net/reader036/viewer/2022083006/56649f325503460f94c4dd2e/html5/thumbnails/12.jpg)
Holt McDougal Algebra 2
2-7 Solving Quadratic Inequalities
Example 4: Problem-Solving ApplicationThe monthly profit P of a small business that sells bicycle helmets can be modeled by the function P(x) = –8x2 + 600x – 4200, where x is the average selling price of a helmet. What range of selling prices will generate a monthly profit of at least $6000?
Pg 114 12-46 even, 48-50,51,53,62-64