Algebra 2 – Quadratic Functions

By Darin Andrews Categories: Algebra, Math
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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:

  1. 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.
  1. 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.

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What Will You Learn?

  • In this algebra 2 lesson on quadratic functions, you will learn the basic principles and properties of quadratic functions, including how to graph them and how to solve quadratic equations. You will also learn how to find the vertex of a parabola and determine its shape and position based on the values of a, b, and c. Through guided and independent practice, you will develop your problem-solving skills and gain a deeper understanding of the concepts covered in the lesson. By the end of the lesson, you will be able to confidently graph quadratic functions and solve quadratic equations using multiple methods.

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