About This Chapter
Advanced Coordinate Geometry - Chapter Summary
Does a parabola sound a little like an alien from another planet? It is actually the U-shaped geometric occurrence you get each time you graph a quadratic equation. In this chapter, you can learn the three different ways to express a parabola, including the standard, vertex and intercept forms.
Graphing equations with differing exponential values in another important skill in coordinate geometry. This chapter reminds you how to pay attention to the local maximums and minimums, or 'hills and valleys', to graph equations. Helpful pointers are included for taking multiple-choice tests that include graphing problems, such as the SAT Subject Test Math 2. All the topics below are included:
- Basics of parabolas
- Parabolas in three forms
- Graphing quartics, cubics and quintics
- Formula, center and radius while graphing a circle
- Hyperbolas and ellipses in graphing
- Polar coordinates and symmetry on graphs
Our video lessons are informative and easy-to-use. They include transcripts of the complete text and tags to locate specific portions for review. The multiple-choice quizzes are good practice for the questions you'll find on the SAT subject test in math.
Advanced Coordinate Geometry Objectives
If math comes easy to you, and you want a chance to showcase your skills, you can take the SAT Subject Test Math 2. Results from this test can be added to your admissions materials to help you get into the college of your choice. Reviewing these concepts on advanced coordinate geometry will help you prepare for the geometry and measurement content area of the test, which represents 28%-32% of the entire test. This subject test has 50 multiple-choice questions on numbers and math operations, algebra, functions, data analysis and probability in addition to geometry and measurement.
1. What is a Parabola?
A parabola is the U shape that we get when we graph a quadratic equation. We actually see parabolas all over the place in real life. In this lesson, learn where, and the correct vocab to use when talking about them.
2. Parabolas in Standard, Intercept, and Vertex Form
By rearranging a quadratic equation, you can end up with an infinite number of ways to express the same thing. Learn about the three main forms of a quadratic and the pros and cons of each.
3. How to Graph Cubics, Quartics, Quintics and Beyond
Finding the graph of a polynomial isn't too hard. If you can graph, you already know the major steps! With a couple rules and helpful memorizing tools, you will be graphing polynomials in no time!
4. Graphing Circles: Identifying the Formula, Center and Radius
Discover how to graph circles by finding key information like the center and radius. Identify circles by simply looking at the formula, and vice versa.
5. 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.
6. 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.
7. Identifying the Line of Symmetry: Definition & Examples
Symmetry can occur in many different ways in mathematics. In this lesson, learn how to identify unique forms of symmetry by finding the line of symmetry.
8. Recognizing Symmetry Graphically, Algebraically & Numerically About the Origin
If you look at flowers and fruits, you'll see that many of these items in nature are symmetrical. In this lesson, learn about symmetry about the origin of a graph. When you are finished, test your knowledge with a short quiz!
9. Recognizing Symmetry Graphically, Algebraically, and Numerically About the X-axis and Y-axis
When you fold a piece of paper exactly in half, you are creating symmetry. Symmetry is found in many areas of mathematics. In this lesson, learn to recognize symmetry graphically, algebraically, and numerically about the x- and y- axes.
10. Graphing Functions in Polar Coordinates: Process & Examples
After watching this video lesson, you will be able to convert any Cartesian coordinate point into a polar coordinate point. You will also learn how to plot these points.
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Other chapters within the SAT Subject Test Mathematics Level 2: Practice and Study Guide course
- Structure & Strategies for the SAT Math Level 2
- Basic Math Review
- Square Roots
- Basic Algebraic Expressions
- Algebraic Linear Equations & Inequalities
- Algebra: Absolute Value Equations & Inequalities
- Algebra: Polynomials
- Functions in Math
- Algebra: Rational Expressions
- Understanding Sequences & Series
- Understanding Exponentials & Logarithms
- Complex and Imaginary Numbers
- Coordinate Geometry Basics
- Coordinate Geometry: Graphing Linear Equations & Inequalities
- Three-Dimensional Geometry
- Overview of Trigonometry
- Probability, Combinations & Permutations
- Working with Data & Statistics
- Basic Mathematical Logic
- Limits of Functions
- SAT Subject Test Mathematics Level 2 Flashcards