General Information
- Subject: Mathematics
- Topic: Quadratics
- Grade/Year: 9 (age 13-14)
- Length of Lesson: 30 minutes
Learning Objectives
By the end of this lesson, students will be able to:
- Define and identify quadratic functions.
- Sketch quadratic functions given their equations.
- Identify the key features of a quadratic function.
- Solve quadratic equations using factoring and the quadratic formula.
- Apply quadratic functions to real-life problems.
Materials
- Whiteboard and markers
- Graph paper
- Quadratic formula handouts
- Factoring handouts
Procedure
Introduction (5 minutes)
- Greet students and introduce the topic of quadratics.
- Review previously learned concepts that are relevant to the lesson (e.g. linear functions).
Quadratic Functions (10 minutes)
- Define quadratic functions and provide examples.
- Show students how to identify a quadratic function from its equation.
- Demonstrate how to sketch a quadratic function on graph paper.
Key Features of Quadratic Functions (5 minutes)
- Identify the key features of a quadratic function, such as vertex, axis of symmetry, and intercepts.
- Discuss the significance of these features in understanding the graph of a quadratic function.
Solving Quadratic Equations (10 minutes)
- Review the process of factoring a quadratic equation.
- Introduce the quadratic formula and show students how to use it to solve quadratic equations.
- Provide examples of quadratic equations and work through them with the class.
Real-Life Applications (5 minutes)
- Present real-life problems that can be solved using quadratic functions.
- Demonstrate how to translate a real-life problem into a quadratic equation.
- Encourage students to think creatively about how quadratic functions can apply to different situations.
Homework (5 minutes)
- Assign homework that reinforces the concepts covered in the lesson.
- Ensure that students understand the expectations and due date for the assignment.
Homework
- Sketch the graph of the quadratic function y=2(x-1)^2-4. Label the key features of the graph.
- Solve the quadratic equation 3x^2+5x-2=0 using factoring.
- A stone is thrown from the top of a building with an initial velocity of 20m/s at an angle of 60 degrees to the horizontal. If the height of the building is 50m, when will the stone reach the ground? (Assume there is no air resistance.)