Lesson Plan for Senior Secondary 1 - Mathematics - olution Of Quadratic Equation By Graphical Method

**Lesson Plan: Solution of Quadratic Equation by Graphical Method** **Grade Level:** Senior Secondary 1 **Subject:** Mathematics **Duration:** 60 minutes **Topic:** Solution of Quadratic Equation by Graphical Method --- ### **Learning Objectives:** By the end of the lesson, students will be able to: 1. Understand the standard form of a quadratic equation. 2. Plot quadratic functions on a graph. 3. Identify the solution(s) to a quadratic equation from the graph. 4. Interpret the significance of the roots in the context of the problem. ### **Materials Needed:** - Graph paper - Graphing calculators or smartphones with graphing apps - Rulers - Pencils and erasers - Whiteboard and markers - Sample quadratic equations for practice ### **Prerequisites:** Students should have a basic understanding of quadratic equations, including their standard form \( ax^2 + bx + c = 0 \), and the concepts of the roots of an equation. --- ### **Lesson Activities:** #### **Introduction (10 minutes)** 1. **Review Quadratic Equations:** - Briefly review what a quadratic equation is and its standard form \( ax^2 + bx + c = 0 \). - Explain that there are several methods to solve quadratic equations, including factoring, completing the square, and using the quadratic formula. 2. **Introduction to Graphical Method:** - Explain that today’s lesson will focus on solving quadratic equations graphically by plotting the corresponding functions on a graph. #### **Activity 1: Plotting Quadratic Functions (20 minutes)** 1. **Example Demonstration:** - Take a sample quadratic equation, for example, \( y = x^2 - 4x + 3 \). - Create a table of values for \( x \) ranging from -2 to 5, calculating the corresponding \( y \) values. - Plot the points on the graph paper. - Draw the curve of the quadratic function. 2. **Class Participation:** - Ask students to assist in plotting the points on the graph. - Encourage discussion about the shape of the graph and the key features (vertex, axis of symmetry, direction of opening). #### **Activity 2: Finding the Roots Graphically (15 minutes)** 1. **Identifying Roots:** - Explain that the roots of the quadratic equation are the \( x \)-coordinates where the curve intersects the \( x \)-axis (where \( y = 0 \)). - On the graph, identify these points of intersection and note them down. 2. **Class Exercise:** - Provide another quadratic equation, \( y = x^2 + 2x - 3 \). - Have students individually create a table of values, plot the graph, and identify the roots. - Circulate to assist and check for understanding. #### **Activity 3: Interpretations and Applications (10 minutes)** 1. **Real-World Application:** - Discuss how the roots of the quadratic function represent solutions to real-life problems (e.g., projectile motion, maximizing area). - Provide an example problem where interpreting the roots is necessary. 2. **Discussion:** - Encourage students to share their understanding and any difficulties they faced. - Discuss how different forms of the quadratic equation affect the graph. #### **Conclusion and Summary (5 minutes)** 1. **Recap Key Points:** - Summarize the steps for plotting a quadratic function and finding the roots graphically. - Emphasize the importance of accuracy in plotting points and drawing the curve. 2. **Next Steps:** - Give a brief overview of other methods for solving quadratic equations, leading into subsequent lessons. - Assign a few quadratic equations for homework where students will practice plotting and finding roots graphically. --- ### **Assessment:** - Observe student participation and understanding during the class exercises. - Review the accuracy of students’ graphs and their ability to identify the roots. - Evaluate students’ homework for correct plotting and interpretation of the quadratic functions. ### **Homework:** 1. Plot the quadratic function \( y = 2x^2 - 4x - 6 \) and find the roots graphically. 2. Write a short paragraph explaining the significance of the roots in one of the problem-solving contexts discussed in class. ### **Additional Resources:** - Online graphing tools (Desmos, GeoGebra) - Textbook references on quadratic equations and their graphs --- This lesson plan integrates interactive activities and practical applications to ensure students understand and can apply the method of solving quadratic equations graphically.