About This Chapter
Geometric Graphing Functions - Chapter Summary
The lessons in this chapter will allow you to learn how to graph functions by plotting points, determine the point-slope form of the equation of a line and understand the use of the midpoint formula. When you have finished, you will be familiar with the following topics:
- Graphing functions by plotting points
- Using and graphing standard form linear equations
- Finding and applying the intercepts of a line
- Graphing undefined slope and zero slope
- The point-slope formula
- How to use the distance and midpoint formulas
- Definition of a parabola and its forms
- Graphing polynomials
Experienced instructors explain each concept in these concise lessons and use real-life examples to make their points clear. You can test your knowledge with the self-assessment quizzes and rewatch the entire lesson, or just certain parts, to reinforce what you've learned.
Geometric Graphing Functions Chapter Objectives
Many beginning students at California State University take the ELM as a means of assessing their mathematics skills. The ELM contains 50 multiple-choice questions, with a 90-minute time limit. Questions on graphing functions are in the Geometry section, which makes up about 30% of the entire test. Topics covered in this chapter that appear on the test include:
- Graphing a function by plotting points determined by an algebraic expression
- Graphing linear and quadratic functions
- Determining the midpoint of a line segment
1. 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.
2. 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.
3. Linear Equations: Intercepts, Standard Form and Graphing
Do you know what to do if an equation doesn't look like y=mx+b?! If not, then this video is for you. Chances are the equation is in standard form, so we'll learn how to use standard form equations, how to graph them and why they can be helpful.
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 within the Basic Geometry: Help & Review course
- Introduction to Basic Geometry
- Geometry Topics
- Basic Geometry: Lines & Angles
- Basic Geometry: Polygons
- Basic Geometry: Triangles
- Basic Geometry: Quadrilaterals
- Basic Geometry: Circles
- Basic Geometric Constructions
- Basic Geometry: Similar Figures
- Basic Geometry: Perimeter, Circumference & Area
- Basic Geometry: 3-Dimensional Figures
- Lines and Angles in Geometry
- Perimeter, Area & Volume
- Geometric Properties of Objects
- Geometric Graphing Basics