GRAPHS AND RELATED TOPICS

Lines

 Graphs of linear equations are used frequently both in Algebra and in the real world.  Having an understanding of graphs of linear equations is very important in mathematics.  Learn how to graph lines in various manners. Learn how to create equations of lines given different attributes. Understanding slope is also an important part of graphing linear equations.

Graph Horizontal and Vertical Lines
Graph Given Intercepts
Graph by Finding Intercepts
Graph Using Slope-Intercept Form - Positive Slope
Graph Using Slope-Intercept Form - Negative Slope
Graph by Getting into Slope-Intercept Form
Graph from Point Slope Form
Find the Slope Given Two Points
Find the Equation of a Line Given a Point and the Slope
Find the Equation of a Line Given Two Points
Find the Equation of a Line Parallel to Another Line
Find the Equation of a Line Perpendicular to Another Line
Application: Find Equation of Line

Regression

 Regression is very important in the real world. Often times we have a lot of data, and want to see if there are any patterns in the data. We often come up with mathematical models for various situations. Below, learn how to find many types of regression, including linear, quadratic, and cubic. More types will be added.

Linear Regression and Correlation Coefficient TI-84
Linear Regression and Correlation Coefficient in the TI-Nspire
Linear Regression and Correlation Coefficient in Desmos
Line of Best Fit and Making Predictions in TI-84
Scatter Plot and Correlation Coefficient in the TI-Nspire
Linear Regression and Making Predictions in the TI-Nspire
Quadratic Regression TI-84
Quadratic Regression TI-Nspire
Quadratic Regression in Desmos
Cubic Regression in TI-84
Cubic Regression in TI-Nspire
Cubic Regression in Desmos

Absolute Value

The graph of an absolute value equation is always a V shaped graph. If you know the parent function for an absolute value equation and how the different transformations work, graphing is very easy. Technology can also be used to help graph an absolute value equation. 

Parent Function for Absolute Value
Graph Absolute Value Equations Using Translations
Graph Absolute Value with a Vertical Stretch or Compression

Quadratic

The graph of a quadratic equation is called a parabola. Parabolas are used often in the real world, especially when calculating trajectories. Learn how to graph parabolas using several methods, as well as with technology.

Graph a Quadratic in Vertex Form Using Translations
Vertical Stretches or Compressions of Quadratic Graphs
Using Vertex and Intercepts to Graph
Using Intercepts to Graph a Quadratic Function
Graph a Parabola Using Vertex and Intercepts (down)

Piecewise Functions

Piecewise functions use different equations for different intervals of the graph. To determine which equation or function to use, you must look at the given interval. Any x-value, contained in that interval, is plugged into the corresponding equation. The graphs of these functions can have breaks and holes in them. They do not have to be a continuous function, and often aren't. Piecewise functions can have as few as two pieces, but can have as many equations as needed.

Graph a Piecewise Function Ex 1
Graph a Piecewise Function Ex 2

Circles

A circle is all points that are equidistant from a point called the center. There are two different formulas for circles, standard form and general form. Learn how to write equations of circles in both forms and how to graph a circle from both forms.

Write the Equation of a Circle in Standard Form
Write the Equation of a Circle in General Form
Graph from Standard Form
Graph from General Form

Extrema

Extrema represent the extreme points of a graph. They are also known as the maximum (maxima if more than one) and the minimum (minima if more than 1). There can be local maxima or minima, which occur when for a set interval they are the highest or lowest point, but not the highest or lowest point of the entire graph. The absolute maximum or minimum occur at the absolutely highest or lowest point respectively on the graph. It is possible for a graph to not have any extrema, and to have multiple combinations of maxima and/or minima. The maxima or minima are always the y-coordinate of that point, since the y-axis represents the up/down movement of the graph. The following videos show how to find these points.

Extrema Defined
Finding Extrema Ex 1
Finding Extrema Ex 2
Find Maximum of a Quadratic Function
Finding Minimum of a Quadratic Function
Finding Minimum of a Quadratic Function with TI-84
Finding Minimum of a Quadratic Function with TI-Nspire
Finding Minimum of a Quadratic Function with Desmos
Finding Maximum of a Quadratic Function TI-84
Finding Maximum of a Quadratic Function with TI-Nspire
Finding Maximum of a Quadratic Function with Desmos

Asymptotes

 Asymptotes are a line that a graph gets closer and closer to, but never actually touches. Look at the rules for finding vertical, horizontal, and oblique asymptotes of rational functions.

Asymptotes of a Rational Function Ex 1
Asymptotes of a Rational Function Ex 2
Asymptotes of a Rational Function Ex 3

Attributes of Graphs

 Learn how to find x and y intercepts of given graphs. How to identify if the graph is increasing, decreasing or constant. Also, the videos will show how to find domain and range, and if the graph is even, odd, or neither.

Find Information about a Given Graph Ex 1

Symmetry

 Symmetry means the graph is the same on both sides. Their are many forms of symmetry in mathematics.
We will look at several types. Mainly we will look at x-axis symmetry, y-axis symmetry, and symmetry with respect to the origin.

Symmetry with Respect to X-axis, Y-axis, or Origin
Test for Symmetry Algebraically Ex 1
Test for Symmetry Algebraically Ex 2

Distance and Midpoint Formulas

 Learn how to use both the distance and midpoint formulas. Both of these formulas are useful in several branches of mathematics. The distance formula is essentially the Pythagorean Theorem. The midpoint formula is just the average of the coordinates.

Find the Midpoint Between Two Points
Find the Distance Between Two Points
Distance Formula-Points Form a Right Triangle