About This Chapter
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.
You'll learn all of the algebra topics covered in the textbook chapter, including:
- Transforming exponential functions
- Quadratic functions
- 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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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Other chapters within the Harcourt On Core Mathematics - Algebra 1: Online Textbook Help course
- On Core Mathematics Algebra 1 Unit 1: Algebraic Modeling and Unit Analysis
- On Core Mathematics Algebra 1 Unit 2: Linear Equations and Inequalities
- On Core Mathematics Algebra 1 Unit 3: Systems of Equations and Inequalities
- On Core Mathematics Algebra 1 Unit 4: Linear Functions
- On Core Mathematics Algebra 1 Unit 5: Exponential Functions
- On Core Mathematics Algebra 1 Unit 6: Piecewise and Absolute Value Functions
- On Core Mathematics Algebra 1 Unit 8: Quadratic Functions of the Form of f(x) = ax^2 + bx + c
- On Core Mathematics Algebra 1 Unit 9: Data Analysis