## About Course

Lesson Objectives:

- To understand the basic principles and properties of quadratic functions
- To learn how to graph quadratic functions
- To learn how to solve quadratic equations

Materials Needed:

- Graph paper
- Calculator
- Whiteboard and markers

Introduction: Begin the lesson by reviewing the concept of a function and how to graph linear functions. Then, introduce the concept of a quadratic function as a function of the form f(x) = ax^2 + bx + c. Explain that the graph of a quadratic function is a parabola, and that its shape and position can be determined by the values of a, b, and c.

Direct Instruction:

- Graphing Quadratic Functions:

- Explain that the vertex of a parabola is the point where it changes direction, and that it is located at the point (-b/2a, f(-b/2a)).
- Demonstrate how to graph a quadratic function by finding the vertex and a few other points, then connecting them to create the parabola.
- Give examples of different quadratic functions and have students graph them on their graph paper.

- Solving Quadratic Equations:

- Explain that a quadratic equation is an equation of the form ax^2 + bx + c = 0, and that it can be solved by factoring, using the quadratic formula, or completing the square.
- Demonstrate how to solve a quadratic equation by factoring, then have students practice solving equations using this method.
- Introduce the quadratic formula and demonstrate how to use it to solve a quadratic equation. Have students practice using the quadratic formula to solve equations.

Guided Practice: Divide students into pairs and have them work together to graph a quadratic function and solve a quadratic equation. Provide feedback and assistance as needed.

Independent Practice: Assign homework that includes several quadratic functions to graph and quadratic equations to solve. Collect and grade the homework to assess student understanding.

Closure: Review the key concepts covered in the lesson, and have students share any questions or insights they gained from the lesson.

Assessment: Assess student understanding through homework assignments, quizzes, and exams. Use a rubric to evaluate their graphing and problem-solving skills.

Extension: Challenge advanced students to explore more complex quadratic functions, such as those with a coefficient other than 1 for the x^2 term. Have them explore the properties of these functions and compare them to the properties of standard quadratic functions.