About This Chapter
Honors Algebra 1: Pre-Calculus Geometry - Chapter Summary and Learning Objectives
Use these lesson videos to learn new skills that will allow you to decipher and graph the equations of circles. In these lessons, our expert instructors will explain the processes of completing the square of an equation, how to use the distance formula, how to use the midpoint formula and the Pythagorean theorem. Make sure to also read the lesson transcripts, after these lesson videos, to reinforce your understanding of:
- Graphing circles and circle formulas
- Uses of the processes of completing the square
- The distance formula and midpoint formula
- Solving geometry problems with visualization
- Using the Pythagorean theorem to find distance
|Graphing Circles: Identifying the Formula, Center and Radius||Learn how to graph circles and identify their properties using a formula.|
|Write the Standard Form of an Equation by Completing the Square||Rewrite quadratic equations to make them easier to solve.|
|How to Use The Distance Formula||Find the distance between two points on a graph.|
|How to Use The Midpoint Formula||Find the midpoint of line segment on a graph.|
|How to Solve Visualizing Geometry Problems||Translate complex problems into visual representations to solve them.|
|Finding Distance with the Pythagorean Theorem||Learn how to use the Pythagorean theorem to find distances.|
1. 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.
2. Write the Standard Form of an Equation by Completing the Square
In math, we have a process called completing the square where you take your quadratic equation and rewrite it to make it easier to solve. Watch this video lesson to learn how you can do this process easily yourself.
3. How to Use The Distance Formula
You can't always rely on your smartphone to tell you how far you need to travel to get from point A to point B. The distance formula will tell you the distance between any two points on a graph. In this lesson, you'll learn where it comes from and how to use it!
4. How to Use The Midpoint Formula
The formula for the midpoint of a line segment will tell you how to find the middle of any line segment on the x, y plane. Learn about this formula and see how it is used to find the midpoint of a line segment.
5. How to Solve Visualizing Geometry Problems
A picture is worth a thousand words, but sometimes drawing that picture can be like doing origami with your eyes closed. Practice translating complex problems into simple, meaningful images in this lesson.
6. Finding Distance with the Pythagorean Theorem
How much faster is it to cut the corners in a race around the block? In this lesson, review the Pythagorean Theorem, and figure out how to solve without a right triangle.
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Other chapters within the Honors Algebra 1 Textbook course
- Honors Algebra 1: Basic Arithmetic Review
- Honors Algebra 1: Fractions & Decimal Review
- Honors Algebra 1: Calculations, Ratios, Percent & Proportions
- Honors Algebra 1: Properties of Real Numbers
- Honors Algebra 1: Exponents & Scientific Notation
- High School Algebra: Radical Expressions
- Honors Algebra 1: Composing Algebraic Equations & Expressions
- Honors Algebra 1: Solving Algebraic Expressions & Equations
- Honors Algebra 1: Properties of Functions
- Honors Algebra 1: Absolute Value Expressions & Equations
- Honors Algebra 1: Matrices in Linear Equations
- High School Algebra: Working With Inequalities
- High School Algebra: Properties of Exponents
- High School Algebra: Properties of Polynomial Functions
- Honors Algebra 1: Vectors in Linear Algebra
- High School Algebra: Complex and Imaginary Numbers
- High School Algebra: Algebraic Distribution
- Honors Algebra 1: Linear Equations
- High School Algebra: Factoring
- Honors Algebra 1: Factoring with FOIL, Graphing Parabolas & Solving Quadratics
- Honors Algebra 1: Graphing & Factoring Quadratic Equations
- High School Algebra: Rational Expressions
- High School Algebra: Cubic Equations
- Honors Algebra 1: Descriptive Statistics
- Honors Algebra 1: Data Analysis
- Honors Algebra 1: Probability & Statistics
- Honors Algebra 1: Units of Measurement in Geometry
- Honors Algebra 1: Shapes of Geometry
- Honors Algebra 1: Similar Polygons
- High School Algebra: Well-Known Equations
- Honors Algebra 1: Maximum & Minimum Value of Functions
- Honors Algebra 1: Patterns in Math