# Ch 15: Graphing Functions

### About This Chapter

## Graphing Functions - Chapter Summary

Learn about the foundations of graphing with the lessons in this chapter. Descriptions of the various parts of graphs, such as x-coordinates, y-coordinates, quadrants and origin are included, along with the x- and y-intercepts. The lessons also explain parabolas and present them in three various forms. The following topics are all included in this study of graphing:

- Elements of graphs and graphing functions
- Linear, increasing, decreasing, positive and negative functions
- Slopes and intercepts of lines
- Point-slope, distance and midpoint formulas
- Standard, intercept and vertex forms of parabolas
- Cubics, quartics and quintics in graphs

Each of the lessons contains a video, text transcript and short, multiple-choice quiz. Feel free to use the lessons as many times as you want to prepare for the NY Regents Algebra Exam. After taking a quiz, if you wish to go back and review a specific portion of a video, you can use the handy video tags to locate just the right spot. Many of the lessons also have links to text-only lessons for additional support on key terms and topics.

### Integrated Algebra Regents Exam Objectives

The state of New York requires that high school students pass a group of five tests by earning no less than a score of 65 on each. This test is one of the approved math options and will be renamed Algebra I as the state furthers its transition to the Common Core Learning Standards.

This three-hour exam assesses your understanding of concepts including functions, number and quantity, statistics and probability and algebra. The section pertaining to algebraic topics involves 50%-56% of the total possible points. The test questions are multiple choice and free response, for which experience with our online quizzes can be an asset.

### 1. What Are the Different Parts of a Graph?

Being able to read a graph isn't just vital for an algebra class. Graphs and charts are used everywhere! We'll take a crash course on the basic x/y plane used in algebra and the fundamental vocab you need.

### 2. Graph Functions by Plotting Points

Let's say you have a function. What does it look like? How do you graph it? In this lesson, we'll learn how to graph functions by determining and plotting points.

### 3. Identify Where a Function is Linear, Increasing or Decreasing, Positive or Negative

Functions do all kinds of fun things. In this lesson, learn how to identify traits of functions such as linear or nonlinear, increasing or decreasing and positive or negative.

### 4. How to Find and Apply The Slope of a Line

In this lesson, we'll discover all about the slopes of lines. We'll learn about different types of slopes and how to find the slopes of lines. We'll use two methods: the slope formula and the slope-intercept form.

### 5. How to Find and Apply the Intercepts of a Line

How can you take an equation of a line and find out where it will cross the x- or y-axis? In this lesson, we'll define x-intercepts and y-intercepts and learn how to find them.

### 6. Graphing Undefined Slope, Zero Slope and More

There are two special cases when it comes to slopes on the xy plane: horizontal and vertical lines. Without any more information, these examples can be pretty confusing. But with a little instruction, they end up being some of the easiest lines to graph!

### 7. Equation of a Line Using Point-Slope Formula

It's time for a road trip to Las Vegas, and after four hours of driving at 60 mph ... Are we there yet? Learn the point-slope form of the equation of a line to help answer this age-old question.

### 8. 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!

### 9. 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.

### 10. 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.

### 11. 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.

### 12. 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!

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### Other Chapters

Other chapters within the NY Regents Exam - Integrated Algebra: Test Prep & Practice course

- Number Theory & Basic Arithmetic
- Problems with Decimals and Fractions
- Problems with Percents
- Problems with Exponents
- Problems with Exponential Expressions
- Problems with Radical Expressions & Equations
- Problems with Algebraic Expressions and Equations
- Distributing Terms in Algebra
- Algebraic Linear Equations & Inequalities
- Understanding Matrices & Absolute Value
- Overview of Functions
- Factoring with Variables
- Quadratics & Polynomials
- Rational Expressions & Practice
- Calculations with Ratios, Percent & Proportions
- Understanding Sets
- Understanding Probability & Statistics
- Factorials & the Binomial Theorem
- Working with Data
- Well-Known Equations
- Intro to Trigonometry
- Measurement for Algebra Students
- Geometry for Algebra Students
- About the NY Regents Examinations
- NY Regents Exam - Integrated Algebra Flashcards