3OverviewIn this module you will be introduced to functions, as well as learning about a class of functions called linear and quadratic. You will also be given access to some tools that are necessary to understand functions.Linear functions describe the relationship between the independent (x) variable and the dependent (y) variable that when graphed creates a line.Quadratic functions describe the relationship between the independent variable (x) and the dependent variable (y) that when graphed create a parabola. These functions are polynomials with a second degree.There is a green star on each of the topic slides. Clicking on this start will return you to the beginning of the presentation. Each webpage is hyperlinked to open right from this presentation as well.
4Topic: Overview of Functions What is a function?How do you determine if something is a function?Domain of a FunctionRange of a FunctionFunction NotationBuild FunctionsTools of the quadratic equationsRadicalsAdding and Subtracting RadicalsMultiplying and Dividing RadicalsSimplifying RadicalsComplex NumbersUseful websites:Graphing Calculator OnlinePrintable Graph Paper
5Topics - Linear Functions SlopeIntercepts (x and y)Horizontal vs. Vertical Lines - Which is a function?Point-Slope FormSlope-Intercept FormStandard FormParallel LinesPerpendicular LinesLinear Inequalities
6Topics - Quadratic Functions Quadratic Equation - DefinitionsExploring the quadratic equationWhat is a quadratic function?What does a quadratic function look like?Focus & DirectrixParabolaGraphing ParabolasGraphing with a graphing calculatorGraphing quadratics in vertex formSolving Quadratic functionsFactoringCompleting the SquareQuadratic FormulaComplex QuadraticsQuadratic Inequalities
7What is a Function? Meat-A-Morphosis Meat-A-Morphosis You Tube VideoJason ErmerThis quick video demonstrates a ‘Function Machine’ using a real life example, as well as demonstrating mathematical examples.
8Recognizing a Function Function: Yes or No?Recognizing a FunctionTesting if a relationship is a functionKhan AcademyThis webpage gives a quick, precise description of how to test is a relation is a function.There are many videos, all listed on the left, that show different ways to test if a relation is a function.
9Domain vs. Range Domain vs Range Graphing, Domain and Range of FunctionsRegents Test PrepThis webpage explains the definition of domain and range, specifically in relationship to graphing.
10Function Notation Function Notation Functions & Function Notation Khan AcademyThis webpage on Khan Academy provides another description of functions. This description of functions also goes into detail about how to use function notation.Please note that there are several different videos (all listed on the left side of the page).Also, please remember that f(x) is function notation.
11Building Functions Building Functions Mathematical Models, Building FunctionsSchool TubeThis video goes into detail showing numerous examples of building functions.The initial examples show how to build functions from values.The remaining examples show how to build functions from other functions.
12Desmos Calculator (Graphing) Graphing Calculator - Ad free Online Graphing CalculatorDesmos Calculator (Graphing)Desmos CalculatorThis online graphing calculator allows (majority) of the features of a hand held graphing calculatorIf you wish to save your functions, you can create a username.Graphing CalculatorThis graphing calculator does not allow points to be plotted in conjunction with the equationThere are no adsGraphing Calculator - Ad free
13Printable Graph Paper Worksheet Works Printable Graph Paper This website allows customizable graph paper to be created, printed, and used for educational purposes.Once you are on this website, type graph paper in the search box to select the type of graph paper you want.
14Square Roots and Radicals Simplifying Radicals REMEMBER: CLICK BACK TO GET BACK TO THIS PRESENTATION ONCE YOU HAVE VISITED THE RESOURCE!Multiplying & Dividing RadicalsAdding and Subtracting Radicals
15Adding and Subtracting Radicals Khan AcademyThis resource provides information on how to add and subtract radicals.
16Multiplying and Dividing Radicals Multiplying and Dividing Radicals: The Math PageThis resource provides examples on how to multiply and divide radicals.There are links to further resources and examples from this site.
17Simplifying Radicals Simplifying Radicals Square Roots & RadicalsSimplifying RadicalsSimplifying RadicalsMath MeetingThis website provides a video that explains how to analyze and simplify radicals, including square rootsSimplifying Radicals: Introduction and SimplificationPurple MathThis site provides an overview to simplifying radicals. It has a video as well as reading material to support the topic.There is a link to a self test as well as a link to extra problems for practiceSimplifying Radicals
18Complex Numbers Complex Numbers Complex Numbers Khan AcademyThis webpage has a detailed explanation of complex numbers. There are also many video showing examples.There are interactive problems to try (all listed on the left hand side of the page).
19Slope Slope of a Line Slope of a Line The Math Open Reference ProjectThis interactive website provides a description of slope, how to find slope, and what a lines looks like with a positive, negative, undefined, or zero slope.There is a practice portion where the user can create different lines to discover how slope changes.
20Intercepts X and Y Intercepts X and Y Intercepts Khan AcademyThis webpage includes a video explanation of x and y intercepts.There are also examples shown of how to graph using the intercepts, as well as how to find the intercepts given an equation in different forms.
21Horizontal & Vertical Lines The Open Math ReferenceThis interactive website provides an explanation of horizontal and vertical lines.There is also an interactive applet that allows the user to explore with vertical and horizontal lines.
22Point-Slope Form of a Line Khan AcademyThis webpage describes from where point slope form of a line develops, shows examples of how to exact the point and slope from an equation, as well as how to write an equation of a line in point slope formThere are interactive examples with answers.
23Slope-Intercept Form of a Line Equation of a Line - Slope Intercept FormThe Math Open Reference ProjectThis interactive website outlines the slope-intercept form of a line. There is also a portion that allows the user to see how the slope and intercept affect the look of the line.y = mx + b
24Standard Form of a Line Standard Form of a Line Standard Form Equation of a LineMath WarehouseThis webpage describes the standard form of line including a video showing an example.There are also examples of how to write and manipulate the equation of a line, including steps and answers.
25Parallel Lines Parallel Lines Parallel Lines The Math Open Reference ProjectThis resource provides a definition of parallel lines as well as an interactive applet to allow for the user to manipulate points and viewing their effect on the slope.There are 2 example problems given.This site provides hints and guidance for the user on how to use the page to further their understanding.There are links at the bottom of this page to other coordinate geometry topics.
26Perpendicular Lines Perpendicular Lines Perpendicular Line The Math Open Reference ProjectThis resource provides a definition of perpendicular lines as well as an interactive applet to allow for the user to manipulate points and viewing their effect on the slope.There are 2 example problems given.This site provides hints and guidance for the user on how to use the page to further their understanding.There are links at the bottom of this page to other coordinate geometry topics.
27Linear Inequalities Practice Problems Math PlanetThis resource provides an information on solving linear inequalities.There are links on the right hand side to take the learner to solving compound inequalities, systems of inequalities, solving absolute value inequalities, and linear inequalities in 2 variables.Shodor.orgThis resource provides an interactive applet to practice graphing inequalities.Practice Problems
28Quadratic Equation Quadratic Equation Quadratic Equation: Wolfram AlphaThis site provides a definition of the quadratic equation including links to terms such as complex numbers, quadratic formulas and completing the square
29Quadratic Equation Quadratic Equation Math is Fun: Quadratic Equation This site provides explanations of the quadratic equation, explains ways to solve the quadratic equation.The site includes interactive applets for exploration as well as an equation solver app.A song to remember the quadratic formula is on this siteAdditional practice questions are at the bottom of this site.
30: What is a Quadratic Function Virtual Nerd VideoThis video provides an overview of what a quadratic function is.This resource provides links to other tutorials such as:What is a functionDefinition of a quadratic function (parabola)Simplifying expressionsWhat is standard form of a quadratic?
31Parabola: Focus and Directrix Parabola OverviewParabola: Focus and Directrix VideoThe Khan AcademyThis Khan Academy Video provides an overview of the focus and directrix of a parabola.
32Graphing Parabolas Graphing Parabolas How to Graph a Parabola NY State RegentsThis site provides 2 examples of how to graph a parabola including information on an equation in quadratic form, axis of symmetry and maximum and minimum.There is a link at the top of the site to additional topics: Algebra Index and Topic IndexThere is a link at the top of the site to the Regents Exam Prep CenterThere is a link at the bottom of the site page to Graphing Calculator Help.
33Graphing with a Calculator Using the TI-83/84 to Graph a ParabolaGraphing with a CalculatorUsing the TI-83/84 to graph a ParabolaThis website provides instructions on how to use the TI-83/84 graphing calculator to graph a parabola. It includes information about the setting the window as well as typing in the quadratic function.
34Graphing Parabolas Graphing Parabolas Khan Academy Video: Graphing Parabolas in vertex formThis video provides an overview of how to graph parabolas in vertex form.
35Completing the Square Completing the Square Khan Academy Video: Completing the SquareVideo demonstrating how to use completing the square on any quadratic equation.
36Quadratic Formula Quadratic Formula Khan Video: Quadratic FormulaThis video provides an overview of how to use the quadratic formula to solve quadratic functionsQuadratic FormulaFree Math Help: Quadratic FormulaThis site provides instructions for using the quadratic formula.There is an interactive problem solving tool available on this site.
37Solve Quadratics by Factoring Hard Case Examples Purple MathSolving quadratic functions by factoringThis site provides examples of how to solve quadratics by factoring. There is a video as well as step by step examples for the reader to follow.There are embedded links for the if the reader needs additional hints or help with the example problems.Solving hard cases : solving quadratics by factoringHard case examples; including what to do when the leading coefficient is -1Hard Case Examples
38Complex Numbers Complex Numbers Math is Fun: Complex Numbers This site is provides an overview of complex numbers including some practice problems.
39Quadratic Inequalities Quadratic Inequalities: Math is FunThis resource provides some colorful examples of how to work with quadratic inequalities.There are real world examples provided as well as links at the bottom to more topics(solving inequalities, inequalities, and other algebra topics)