MODULE 6

• DISCIPLINE • GOOD TASTE • EXCELLENCE
• Writer: Alden O. Madregalejo
• Cover Illustrator: Joel J. Estudillo
• Department of Education National Capital Region SCHOOLS DIVISION OFFICE MARIKINA CITY
• MATHEMATICS Quarter 1 – Module 6: Quadratic Inequalities
• What I Need to Know


  Know Illustrate quadratic inequalities, solve quadratic inequalities, and solve problems involving quadratic inequalities in one variable
• Mathematical symbols

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• The mathematical sentences are inequalities EXCEPT for the one that is an equality
• Quadratic inequalities in one variable are in the form ax^2 + bx + c < 0, ax^2 + bx + c > 0, ax^2 + bx + c ≤ 0, or ax^2 + bx + c ≥ 0, where a, b, and c are real numbers and a ≠ 0
• Quadratic inequality


  Mathematical sentence involving a quadratic expression and an inequality symbol
• Solving quadratic inequalities in one variable

  1. Find the boundary point/s by getting the roots of the corresponding equation

  2. Plot the boundary point/s on the number line

  3. Use the Point-Test Method by getting the coordinate of point that lies along each part of the number line

  4. Evaluate the given inequality using the coordinate of each point

  5. Write the solution set in either set builder notation or interval notation
• Inequality symbols are represented visually on the number line using circles and arrows
• Inequality symbols and their visual representations

  • Greater than (>) - open circle with arrow to the right
  • Less than (<) - open circle with arrow to the left
  • Greater than or equal to (≥) - closed circle with arrow to the right
  • Less than or equal to (≤) - closed circle with arrow to the left
• Solution set of quadratic inequality with less than (<)


  In between the roots, written in set builder notation {x/r1 < x < r2} and interval notation (r1, r2)
• Solution set of quadratic inequality with less than or equal to (≤)


  In between the roots inclusive, written in set builder notation {x/r1 ≤ x ≤ r2} and interval notation [r1, r2]
• Solution set of quadratic inequality with greater than (>)


  Apart from the roots, written in set builder notation {x/(−∞, r1) ∪ (r2, +∞)} and interval notation (−∞, r1) ∪ (r2, +∞)
• Solution set of quadratic inequality with greater than or equal to (≥)


  Apart from the roots, written in set builder notation {x/(∞−, r1] ∪ [r2, +∞)} and interval notation (∞−, r1] ∪ [r2, +∞)
• How are quadratic inequalities used in real life situations?
• How can quadratic inequalities help you?
• Rectangular parking lot

  Length is 250 m longer than its width, if the area is less than 35,000 m2 and if the required area provided for each car to be parked is 6 m2
• Quadratic inequality in one variable


  Solving problems involving
• Steps to solve quadratic inequality in one variable


  1. Step 1: Set up the inequality

  2. Step 2: Solve the inequality

  3. Step 3: Check the solution

  4. Step 4: Write the final solution
• Word problems are essential in Mathematics and need a deep understanding of the mathematical concepts provided
• Steps to solve word problems

  1. Understand the problem

  2. Plan and represent unknown quantities

  3. Solve the problem

  4. Check the solution
• Quadratic inequalities are useful tools in solving real-life situational problems and in making decisions