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
Graphing a function by plotting points allows for the visualization of all of the points that are used in an equation connect with one another. Learn how to find ordered pairs and also plot and connect points on a graph.
2. Identify Where a Function is Linear, Increasing or Decreasing, Positive or Negative
Functions can appear in the form of opposites, which is one way of identifying what type they are. Discover how a function can be linear or nonlinear, increasing or decreasing, and positive or negative.
3. Linear Equations: Intercepts, Standard Form and Graphing
To solve a linear equation, begin by determining whether it is written in the standard form or the slope-intercept form. Explore the differences between the slope-intercept form and the standard form of a linear equation, and learn how to graph the point of intercept for each.
4. How to Find and Apply The Slope of a Line
The slope of a line refers to how steep it is whether it is positive or negative. Study the definition and types of slopes, learn how to find and apply the slope of a line, and practice using points and equations.
5. How to Find and Apply the Intercepts of a Line
The intercepts of a line can be calculated through the x-intercept and the y-intercept. Learn about intercepts and the definition of x- and y-intercepts, and apply that learning through practice problems.
6. Graphing Undefined Slope, Zero Slope and More
When the variable determining the slope is mathematically impossible but can still be graphed, it is referred to as an undefined slope. Learn how to compute formulas to graphs that have either undefined slope or zero slopes, and discover what this means for the line.
7. Equation of a Line Using Point-Slope Formula
The point-slope formula is composed of a specific point of coordinates and a slope indicating a type of change over a given variable, such as distance over time. Identify the use of point-slope formula in graphing a line through provided examples.
8. How to Use The Distance Formula
The distance formula is a shortened form of the Pythagorean Theorem. Learn about the Pythagorean Theorem and the distance formula, along with examples of how the formula is used.
9. How to Use The Midpoint Formula
The midpoint formula enables us to find the midpoint of a line segment when we know the endpoints. Learn about line segments, midpoints, and how to use the midpoint formula. Explore examples, and understand that the midpoint can be found on both vertical and horizontal line segments.
10. What is a Parabola?
A parabola is a U shape that is created when a quadratic equation is graphed. Explore the characteristics of parabolas, how they are used in everyday life, and the defining spots of a parabola.
11. Parabolas in Standard, Intercept, and Vertex Form
The equation of a parabola can be expressed in three different forms. Explore different kinds of parabolas, and learn about the standard form, the intercept form, and the vertex form of parabola equations.
12. How to Graph Cubics, Quartics, Quintics and Beyond
Following the proper steps, the basic principles of graphing can be applied to cubics, quartics, quintics, and other polynomial functions. Learn more about basic graphing principles for polynomial functions, the importance of local maximums and minimums, and sketching for class on a graph through a detailed practice test question.
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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