Ch 7: On Core Mathematics Algebra 1 Unit 7: Quadratic Functions of the Form of f(x) = a(x-h)^2 + k

About This Chapter

The Quadratic Functions of the Form of f(x) = a(x-h)^2 + k chapter of this On Core Mathematics Algebra 1 Companion Course aligns with the same chapter in the On Core Mathematics Algebra 1 textbook. These simple and fun video lessons are about five minutes long and help you learn the essential lessons about specific functions.

How It Works:

  • Find the lesson within this chapter that corresponds to what you're studying in the Quadratic Functions of the Form of f(x) = a(x-h)^2 + k chapter of your textbook.
  • Watch fun videos that cover the functions concepts you need to learn or review.
  • Complete the quiz after watching each video lesson to test your understanding.
  • If you need additional help, rewatch the videos until you've mastered the material, or submit a question for one of our instructors.

Chapter Topics

You'll learn all of the algebra topics covered in the textbook chapter, including:

  • Transforming exponential functions
  • Quadratic functions
  • Quadratics
  • Vertex form
  • Transforming quadratic functions
  • Solving quadratic equations with graphing
  • Solving with square roots
  • Modeling with quadratic functions

On Core Mathematics is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.

9 Lessons in Chapter 7: On Core Mathematics Algebra 1 Unit 7: Quadratic Functions of the Form of f(x) = a(x-h)^2 + k
Test your knowledge with a 30-question chapter practice test
Transformation of Exponential Functions: Examples & Summary

1. Transformation of Exponential Functions: Examples & Summary

All exponential functions follow a basic graph. But when you make changes to the function, you will see the graph shift and make changes. Watch this video lesson to learn how to easily identify these changes or transformations.

Quadratic Functions: Examples & Formula

2. Quadratic Functions: Examples & Formula

Learn what sets quadratic functions apart from all other functions. Learn how you can spot a quadratic just by looking at its graph. Also learn the two formulas that will help you when working with them.

Vertex Form: Equation & Functions

3. Vertex Form: Equation & Functions

Just as y = mx + b is a useful format for graphing linear functions, y = a(x - h)^2 + k is a useful format for graphing quadratic functions. We will explore its uses and learn how to convert any quadratic equation into vertex form.

Quadratics: Equations & Graphs

4. Quadratics: Equations & Graphs

We will look at quadratic equations: what they are, some forms in which we might find them, how we can put them into standard form, and how their graphs look, including some features of the graphs.

Transforming Quadratic Functions

5. Transforming Quadratic Functions

The basic form of a quadratic function is f(x)=x^2 . The graph is a parabola with a vertex at (0,0) opening up. All other quadratic functions are transformations of this parent function.

Transformations of Quadratic Functions

6. Transformations of Quadratic Functions

In this lesson, we will not only go over the basic definition of a quadratic function, we will also talk about transformations of those functions. In other words, we will discuss how to move the graph around by changing the formula.

How to Solve a Quadratic Equation by Graphing

7. How to Solve a Quadratic Equation by Graphing

This lesson will show us how to solve a quadratic equation by graphing. Through definitions, illustrations, and applications, we will learn the steps involved in this process.

Solving Quadratic Equations with Square Roots or Graphing the Function

8. Solving Quadratic Equations with Square Roots or Graphing the Function

Quadratic equations can be solved in many ways, including taking square roots and graphing the function. In this lesson, learn how to use these techniques to solve quadratic equations.

Modeling with Quadratic Functions

9. Modeling with Quadratic Functions

In this lesson, you will learn how to use a quadratic function in the standard, vertex, and factored forms to model a real-life scenario. You will describe and evaluate a path of a launched object using quadratic modeling.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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