Unit-1-Mod-6-Quadratic-Inequalities.pptx

Unit-1-Mod-6-Quadratic-Inequalities.pptx

• 1.
  LESSON 1.9 QUADRATIC INEQUALITIES
• 2.
  Objectives: At the endof the session, you should be able to:  Illustrate quadratic inequalities;  Solve problems involving quadratic inequalities
• 3.
  Recall: Solving Inequalities: 1. GraphForm 2. Set Form 3. Interval Form
• 4.
  Recall: Solving Inequalities: 1. GraphForm 2. Set Form 3. Interval Form
• 5.
  Recall:
• 6.
  Quadratic Inequalities A quadraticinequality is an inequality of the form: 𝑎 𝑥2 +𝑏𝑥+𝑐 <0 𝑎 𝑥2 +𝑏𝑥+𝑐 ≤ 0 𝑎 𝑥2 +𝑏𝑥+𝑐 >0 𝑎 𝑥2 +𝑏𝑥+𝑐 ≥ 0 Where a, b and c are real numbers with . If a quadratic inequality is factorable, it can be solved using a sign graph. A sign graph shows where each factor is positive, negative or zero.
• 7.
  Summary: Solving QuadraticInequalities Given and Then, the condition of the quadratic inequalities are the following: 𝒂 𝒙𝟐 +𝒃𝒙+𝒄>𝟎 Solution: 𝒂 𝒙𝟐 +𝒃𝒙+𝒄 ≥ 𝟎 Solution: 𝒂 𝒙𝟐 +𝒃𝒙+𝒄<𝟎 Solution: 𝒂 𝒙𝟐 +𝒃𝒙+𝒄 ≤ 𝟎 Solution:
• 8.
  Solve Quadratic Inequalities𝒙𝟐 −𝟓 𝒙 +𝟒>𝟎 𝒂 𝒙𝟐 +𝒃𝒙+𝒄>𝟎 Solution:
• 9.
  Solve Quadratic Inequalities𝒙𝟐 +𝟑𝒙 −𝟒≥ 𝟎 𝒂 𝒙𝟐 +𝒃𝒙+𝒄 ≥ 𝟎 Solution:
• 10.
  Solve Quadratic Inequalities𝟐 𝒙𝟐 +𝒙 −𝟔<𝟎 𝒂 𝒙𝟐 +𝒃𝒙+𝒄<𝟎 Solution:
• 11.
  Solve Quadratic Inequalities𝒙𝟐 −𝟒 𝒙 −𝟏𝟐≤ 𝟎 𝒂 𝒙𝟐 +𝒃𝒙+𝒄 ≤ 𝟎 Solution:
• 12.
  Quadratic Inequalities Solve: 1. Writethe standard form of the equation: Find the critical points of the inequality by equating each factor to zero, then solve for the unknown: 𝑥2 −3 𝑥 ≥− 2 𝑥2 −3 𝑥+2≥ 0 2. Factored form of quadratic equation: (𝑥− 2)(𝑥 −1)≥ 0 Method 1
• 13.
  Quadratic Inequalities Construct atable listing the factors, the product, and interval covering the whole real number line. - + + - - + + - + Since , we look at the column of the interval where the product is positive. Hence, the solution is
• 14.
  Quadratic Inequalities usingsign graph Solve: 𝑥2 −3 𝑥+2 ≥ 0 0 1 2 Method 2 – Sign Graph 𝑥2 −3 𝑥+2 ≥ 0 (𝑥− 2)(𝑥 −1)≥ 0
• 15.
  Quadratic Inequalities usingsign graph Solve: 𝑥2 +3 𝑥 <0 0 1 2 Method 2 – Sign Graph
• 16.
  Quadratic Inequalities usingsign graph Solve: 𝑥2 +𝑥 −6>0 Method 2 – Sign Graph 0 1 2 0 1 2
• 17.
  Quadratic Inequalities usingsign graph Solve: 𝑥2 ≤ 2 𝑥 +8 0 1 2 Method 2 – Sign Graph