**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
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### **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.
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### **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.
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### **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
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This lesson plan integrates interactive activities and practical applications to ensure students understand and can apply the method of solving quadratic equations graphically.