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- 1. A Detailed Lesson Plan in Mathematics IV “Solving Quadratic Inequalities”
- 2. I. Objectives• At the end of the lesson, the students should be able to:• demonstrate the ability to solve quadratic inequalities using the graphic and algebraic method.• internalize the concept of solving problems in different methods.• correctly solve quadratic inequalities.
- 3. II. Subject Matter• Topic: Solving Quadratic Inequlities• References:• Stewart,J., Redlin L., & Watson, S. (2007). Algebra and Trigonometry. Pasig City: Cengage Learning. pp. 122-124• http://www.regentsprep.org/Regents/math/algtrig/ ATE6/Quadinequal.htm• Materials: graphing board
- 4. III. Learning Activities Teacher’s Activity Student’s Activity • Expected response fromA. Preparation students:• Daily Routine• “Let us pray first.” • (One student will lead the prayer)• “Good morning class!” • “Good morning ma’am/sir!”• “Before you take your • (Students will pick up the seat, please pick up the pieces of paper.) pieces of paper under your chair.” • (Students will be sitting• “Thank you class. You may down.) now take your seat.” • (Students will say present as• “Let me have your the teacher calls their name.) attendance. Say present if
- 5. 2. Review• “Before we proceed to our • “Our previous lesson is all next topic let us first have a about solving linear quick review of our previous inequalities.” lesson. So, what was our previous lesson all about?”• “Very good. What do we • “We need to know the need to know in order to rules for inequalities in solve linear inequalities?” order to solve linear• “That’s right. So, what are inequalities.” these three properties that • “Addition Property of we have discussed? Give one.” Inequality”• “Another property? • “Subtraction Property of Inequality”• “Very good! And the last • “Multiplication property one?” of Inequality”
- 6. 3. Motivation• “Class, I will be showing you pictures and observe what • (Students will observe the the similarities of the pictures pictures.) is.” • “The pictures show curves.”• “What can you say about the pictures?” • “They are called parabola.”• “That’s right. What do we call those curves in math?” • (Students will listen• “Since we are talking about attentively.) parabola, these are the graph of quadratic.”• “Today we will be learning how to solve quadratic inequalities. Not quadratic equations because in life, it is not always equal. We also encounter inequality. Like what we usually say or hear, “life is unfair.”
- 7. B. Presentation1. Activity• “Class, could you • (Students perform the please graph x2 + 5x – 6 activity.) ≥ 0 on your notebook.”• “Who would like to • (One student will share their work on the draw the graph on the board?” board.)• “Thank you. That’s correct.”
- 8. 2. Analysis• Class, what do you think is • “When we have x2 + 5x – 6 the difference when we = 0, we will be only solving solved x2 + 5x – 6 ≤ 0 and when the equation is equal x2 + 5x – 6 = 0?” to 0. When we have x2 + 5x – 6 ≤ 0, we will be solving for the values of x when it is equal to 0 and when it is less than 0 like -1, -2 and so on.”• “Very good observation.”
- 9. 3. Abstraction• “Quadratic inequalities can be solved either by the use of the graphic or the algebraic method.”• “Using the graphic • (Students will listen method, let us solve for x2 + attentively.) 5x – 6 ≤ 0. Let us use the graph drawn in the board.”
- 10. • “Each point on the x-axis has a y-axis• “Here are the steps in solving the quadratic inequalities graphically:1. Change the inequality sign to equal sign.2. Graph the equation.3. From the graph, pick a number from each interval and test it in the original inequality. If the result is true, that interval is a solution to the inequality. For example based from our graph:
- 11. • So the answer is x ≤ 1 and x ≥ -6 or• {x │-6 ≤ x ≤ 1}.”• “Let us shade the answers.”• “Take note that when it is ≤ or ≥, we use close dot (●) in plotting points but when it is < or >, we use open dot (○) and broken line to indicate that they are not included as the answer.”• “Now let us use the algebraic method to solve the same inequality x2 + 5x – 6 ≤ 0.”• x2 + 5x – 6 ≤ 0• (x – 1)(x + 6) ≤ 0 Factor
- 12. • “Now, there are two ways this product could be less than zero or equal to 0• (x - 1) ≤ 0 and (x + 6) ≥ 0 or (x - 1) ≥ 0 and (x + 6) ≤ 0. First situation:1. (x - 1) ≤ 0 and (x + 6) ≥ 0 x ≤ 1 and x ≥ -6• This tells us that -6 ≤ x ≤ 1.
- 13. Second situation:(x - 1) ≥ 0 and (x + 6) ≤ 0x ≥ 1 and x ≤ -6• This tells us that 1 ≤ x ≤ -6. There are NO values for which this situation is true.• Final answer: x ≤ 1 and x ≥ -6 or {x │-6 ≤ x ≤ 1}.”• “Using either the graphic or the algebraic method, we arrive at the same answer.”• “The graph of a quadratic inequality will include either the region inside the boundary or outside the boundary. The boundary itself may or may not be included.” • “Yes ma’am/sir.”• “Is it clear?” • “ No”• “Do you have any questions?”
- 14. 4. Application• “Use the graphic and • (Students will solve the algebraic method to inequality.) solve x2 + 8x > -15.”• “Who wants to show their answer on the • (One student will board?” answer on the board.)• “Very good. Can you please explain your • (The student will answer?” explain his/her answer.)
- 15. IV. Evaluation Solve the quadratic inequality. Use both the algebraic and graphic method.1. x2 – 5x + 6 ≤ 02. x2 – 3x – 18 ≤ 03. 2x2 + x ≥ 14. x2 –x – 12 > 0
- 16. V. Assignment Solve the following quadratic inequality by graphic method.1. –x2 + 4 ≤ 02. x2 – 4 ≥ 0 Note:• Graph the two quadratic inequalities in one Cartesian plane.• Shade your solution.• Use different colors in shading the answer in the two quadratic inequalities.

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