About This Chapter
Algebra II: Conic Sections - Chapter Summary and Learning Objectives
Put your graphing and algebraic problem-solving abilities to the test with this chapter on conic sections. Instructors show you how these skills, along with a working knowledge of vertices, foci and directrices, can be used to graph and write equations for conic sections. By the end of this chapter, you should be able to do the following:
- Define ellipse, circle, hyperbola and parabola
- Identify conic sections' foci and vertices
- Graph conic sections centered at various points on the coordinate plane
- Write the equation for a conic section in standard form
|Defining and Graphing Ellipses in Algebra||Learn how to graph ellipses centered at the origin as well as at other points on the coordinate plane.|
|How to Write the Equation of an Ellipse in Standard Form||Examine methods for writing equations of ellipses in standard form.|
|The Circle: Definition, Conic Sections & Distance Formula||Explain how to work with circle conic sections and use the distance formula.|
|The Hyperbola: Definition, Vertices, Foci & Graphing||Learn strategies for graphing a hyperbola after identifying its foci and vertices.|
|How to Write the Equation of a Hyperbola in Standard Form||Find out how to write the equation of a hyperbola in standard form.|
|The Parabola: Definition & Graphing||Get tips for graphing parabolas with vertices at the origin as well as at other points on the coordinate plane.|
|How to Write the Equation of a Parabola in Standard Form||Discover methods for writing a parabola's equation in standard form.|
|How to Identify a Conic Section by Its Formulas||Use formulas to determine whether a conic section is a parabola, hyperbola, circle or ellipse.|
1. Defining and Graphing Ellipses in Algebra
Watch this video lesson to find out what makes ellipses so unique. Learn what kind of shape an ellipse is, how you can create one yourself and how you can graph an ellipse by just looking at the numbers in the equation.
2. How to Write the Equation of an Ellipse in Standard Form
In algebra, we have equations that make our life so much easier. Some equations are able to tell us information without hard math. Watch this video lesson to see how the equation of an ellipse does this.
3. The Circle: Definition, Conic Sections & Distance Formula
Watch this video lesson, and you will learn what makes a circle a conic section. Also learn how to calculate the circumference of a circle. You will learn about the one important measurement that you need for any circle.
4. The Hyperbola: Definition, Vertices, Foci & Graphing
In this video lesson, we'll learn what a hyperbola is and how to graph one using the standard equation to find the center point, vertices and focus points.
5. How to Write the Equation of a Hyperbola in Standard Form
When it comes to equations in algebra, there is most always a standard form that provides us with useful information. Watch this video lesson to learn how to write the standard form equation of a hyperbola by using information about the hyperbola.
6. The Parabola: Definition & Graphing
Watch this video lesson to learn what a parabola is and how you can graph it. Find out how to extract useful information from the standard form equation of a parabola to help you graph it.
7. How to Write the Equation of a Parabola in Standard Form
After watching this video lesson, you will be able to write the equation of a parabola in standard form when given just two important points from the parabola. Learn what these two points are and how they relate to the parabola.
8. How to Identify a Conic Section by Its Formulas
In algebra, we have a formula for everything. Take a cone and slice it and we have a formula for the shape that results. Watch this video lesson to learn how to distinguish between these formulas.
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Other chapters within the Algebra II: High School course
- Algebra II: Real Numbers
- Algebra II: Complex and Imaginary Numbers Review
- Algebra II: Exponents and Exponential Expressions Review
- Algebra II: Properties of Functions Review
- Algebra II: Linear Equations Review
- Algebra II: Systems of Linear Equations
- Algebra II: Inequalities Review
- Algebra II: Absolute Value Review
- Algebra II: Graphing and Factoring Quadratic Equations Review
- Algebra II: Quadratic Equations
- Algebra II: Factoring
- Algebra II: Polynomials
- Algebra II: Rational Expressions
- Algebra II: Graphing and Functions
- Algebra II: Roots and Radical Expressions Review
- Algebra II: Exponential and Logarithmic Functions
- Algebra II: Sequences & Series
- Algebra II: Combinatorics
- Algebra II: Calculations, Ratios, Percent & Proportions Review
- Algebra II: Statistics
- Algebra II: Trigonometry
- Teacher Resources for High School Algebra II