Graphing Quadratic Inequalities, Verifying Solutions.
- 1. 9.7 GRAPHING QUADRATIC INEQUALITIES OBJECTIVE: 1. To verify if a given point is a solution of the quadratic inequality. 2. To graph a quadratic inequality and identify its solution set.
- 2. 9.7 Graphing Quadratic Inequalities Quadratic inequalities may be of the following types: 𝒚 < 𝒂𝒙 𝟐 + 𝒃𝒙 + 𝒄 𝒚 > 𝒂𝒙 𝟐 + 𝒃𝒙 + 𝒄 𝒚 ≤ 𝒂𝒙 𝟐 + 𝒃𝒙 + 𝒄 𝒚 ≥ 𝒂𝒙 𝟐 + 𝒃𝒙 + 𝒄 The graph of the quadratic inequality consists of the graph of all the points 𝒙, 𝒚 that are solutions of the inequality. To verify if a point is a solution of the quadratic inequality, you must evaluate the given in the inequality and check if it is true or false.
- 3. 9.7 Graphing Quadratic Inequalities In the following examples, you will verify if the given point is a solution or not of the inequality. 1. 𝑦 < 𝑥2 +2𝑥 − 4 ; 𝐴 −1, −2 𝐸𝑣𝑎𝑙𝑢𝑎𝑡𝑖𝑛𝑔 𝐴 −1, −2 −2 < −1 2 + 2 −1 − 4 −2 < 1 − 2 − 4 −2 < −1 − 4 −2 < −5 Since the statement is false, the point is not a solution to the inequality. 2. 𝑦 < 𝑥2 + 2𝑥 − 4 ; 𝐵 2,3 𝐸𝑣𝑎𝑙𝑢𝑎𝑡𝑖𝑛𝑔 𝐵 2,3 3 < 2 2 + 2 2 − 4 3 < 4 + 4 − 4 3 < 8 − 4 3 < 4 Since the statement is true, the point is part of the solutions to the inequality.
- 4. 9.7 Graphing Quadratic Inequalities Exercise: verify the given points in the following inequalities. State if the point is a solution or not, of the inequality. 𝟏. 𝒚 ≤ −𝒙 𝟐 − 𝟓𝒙 + 𝟒 ; 𝑷(−𝟏, 𝟐) 𝟐. 𝒚 > 𝟑𝒙 𝟐 + 𝟐𝒙 ; 𝑸(𝟏, −𝟏)
- 5. HOMEWORK: Pg. 551, Exercises 13 to 16
- 6. 9.7 Graphing Quadratic Inequalities The process of verifying points is useful to determine the solution set of any quadratic inequality.
- 7. 9.7 Graphing Quadratic Inequalities
- 8. 9.7 Graphing Quadratic Inequalities Exercise: Graph the following inequality. Identify correctly the solution set. 𝒚 ≥ −𝒙 𝟐 + 𝟑𝒙 − 𝟏
- 9. HOMEWORK: Pg. 552, Exercises 23 to 31