Duration: 1 hour
Objectives:
- To understand what a quadratic equation is and its standard form
- To solve quadratic equations using the quadratic formula
- To graph quadratic equations and understand the meaning of the vertex and axis of symmetry
Materials:
- Whiteboard and markers
- Graphing calculator or graph paper
- Handout with practice problems
Introduction (10 minutes):
- Ask students if they have heard of quadratic equations and what they know about them
- Introduce the standard form of a quadratic equation: y = ax^2 + bx + c
- Explain that a quadratic equation is a polynomial equation of degree 2
Body (35 minutes):
- Demonstrate how to solve quadratic equations using the quadratic formula
- Provide examples for students to solve in pairs or independently
- Discuss the importance of the vertex and axis of symmetry in graphing quadratic equations
- Demonstrate how to graph a quadratic equation using a graphing calculator or graph paper
- Provide practice problems for students to graph in pairs or independently
Conclusion (15 minutes):
- Review the key concepts covered in the lesson
- Answer any questions students may have
- Assign homework (e.g. additional practice problems or a worksheet)
- Summarize what will be covered in the next lesson
Assessment:
- Observe students during the practice problems to assess understanding
- Collect and grade the homework to see how well students have retained the material
handout:
Title: Quadratic Equations and Graphs Practice Problems
Introduction:
In this handout, we will practice solving quadratic equations and graphing quadratic functions. The following topics will be covered:
- Factoring quadratic equations
- Using the quadratic formula
- Graphing quadratic functions using the vertex and intercepts
Practice Problems:
- Factor the following quadratic equation: x^2 + 5x + 6 = 0
- Solve the following quadratic equation using the quadratic formula: x^2 - 4x + 3 = 0
- Graph the following quadratic function using the vertex and intercepts: y = x^2 + 2x + 1
- Find the axis of symmetry, vertex, and y-intercept for the following quadratic function: y = -2x^2 + 4x - 3
- Solve the following quadratic equation by factoring: x^2 - 9x + 20 = 0
Answers:
- (x + 2)(x + 3) = 0
- x = 2 ± √(7)/2
- The vertex is (0, 1) and the x-intercepts are (-1, 0) and (-1, 0).
- Axis of symmetry: x = 2; Vertex: (2, -3); y-intercept: (0, -3)
- x = 5 ± √(15)
Note: These are just examples of practice problems and answers. Depending on the level of your students, you may need to modify the difficulty of the problems or provide more guidance.
