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 +...
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
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
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).
Holt McDougal Algebra 2
2-7 Solving Quadratic Inequalities
Graph y ≥ x2 – 7x + 10.
Example 1: Graphing Quadratic Inequalities in Two Variables
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
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.
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.
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
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.
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
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
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