Quadratic Equations and Functions

Math Examples

Our Math Examples page includes hundreds of worked-out examples for a variety of algebra topics. Far exceeding the handful of examples found in textbooks, our Math Examples allow students to recognize among the solutions to better anchor their understanding of the concept.

• 10 worked-out examples for solving quadratic equations graphically: http://media4math.com/math-examples.asp#QuadraticsGraphically. Includes a quiz and a slide show.
• 4 worked-out example for solving quadratic equations by completing the square: http://media4math.com/math-examples.asp#CompletingSquare. Includes a quiz and a slide show.
• 12 worked-out examples for solving quadratic equations using the quadratic formula: http://media4math.com/math-examples.asp#QuadraticFormula. Includes a quiz and a slide show.
• 11 worked-out examples for factoring quadratics: http://media4math.com/math-examples.asp#FactoringQuadratics. Includes a quiz and slide show.

TI-Nspire Video-Based Tutorials

Our TI-Nspire Mini-Tutorials support the original TI-Nspire Clickpad, the more recent Touchpad, and the new TI-Nspire CX. Each video tutorial shows all keystrokes and also allow for exploration of key math topics.

• Graphs of quadratic functions: http://media4math.com/calculator-mini-tutorials.asp#GraphingQuadraticFunction.
• Exploring quadratic functions in standard form using sliders: http://media4math.com/calculator-mini-tutorials.asp#QuadraticsStandardSliders.
• Exploring quadratic functions in vertex form using sliders: http://media4math.com/calculator-mini-tutorials.asp#QuadraticsVertexSliders.
• Graphs of Quadratic Inequalities: http://media4math.com/calculator-mini-tutorials.asp#GraphingQuadraticInequalities.
• Creating a template to find the roots of a quadratic equation: http://media4math.com/calculator-mini-tutorials.asp#QuadraticFormula.
• CX Mini-Tutorial: Creating a Quadratic Formula Template: http://media4math.com/calculator-mini-tutorials.asp#CXQuadratic1.
• CX Mini-Tutorial: Graphing Quadratic Functions in Standard Form Using Sliders: http://media4math.com/calculator-mini-tutorials.asp#CXQuadratic2.
• CX Mini-Tutorial: Graphing Quadratic Functions in Vertex Form Using Sliders: http://media4math.com/calculator-mini-tutorials.asp#CXQuadratic3.
• CX Mini-Tutorial: Quadratic Regression: http://media4math.com/calculator-mini-tutorials.asp#CXRegression2.

Promethean Flipcharts

Our Promethean Flipchart page includes free and premium downloadable Flipcharts, ready to use in your classroom.

• Free Promethean Flipcharts: http://media4math.com/PrometheanFlipcharts.asp#FreePromethean.
• Algebra Applications Flipcharts: http://media4math.com/PrometheanFlipcharts.asp#AlgebraFlipcharts.
• TI-Nspire CX Library: http://media4math.com/PrometheanFlipcharts.asp#NspirationsFlipcharts.

PowerPoint Presentations and Math Labs

Our PowerPoint Presentations page and our Math Labs provide additional opportunities to review quadratics.

• Algebra Jeopardy PowerPoint: http://media4math.com/PowerPointPresentations.asp#AlgebraJeopardy.
• Math Labs: http://media4math.com/math-labs.asp.

This post was sponsored by iTutor Maths – Online Maths Tutor

Slope Formula

Math Examples

We have 21 worked-out examples for calculating slope under varying conditions: http://media4math.com/math-examples.asp#Slope. Each example shows a worked-out solution, like the one shown here.

Math Solvers

We have a math solver for calculating the slope, given two sets of coordinates: http://media4math.com/MathSolvers/slopeformulasolver.html. But rather than merely calculating the slope, our solvers go through the solution for finding the slope. This provides an excellent opportunity to review the concept.

Videos

1. Here is a brief video introducing the slope formula: http://media4math.com/Examples/SlopeFormula/SlopeExample0.html.
2. If you use the TI-Nspire Clickpad, TouchPad, or CX, here are some videos on slope:
1. Finding the slope of a line connecting two points: http://media4math.com/calculator-mini-tutorials.asp#SlopeTwoPoints and http://media4math.com/calculator-mini-tutorials.asp#CXSlope.
2. Creating a slope formula template using the programming capabilities of the Nspire: http://media4math.com/calculator-mini-tutorials.asp#SlopeFormulaTemplate
3. We have a video-based Math Lab, hands-on activity exploring slope: http://media4math.com/math-labs.asp.

Promethean Flipcharts

1. One of our Promethean Flipcharts for Algebra focuses on an application of slope, cycling: http://media4math.com/PrometheanFlipcharts.asp#AlgebraFlipcharts.

Math in the News: 9/19/11

In our current issue of Math in the News we look at the geometry of the Freedom Tower at 1 World Trade Center. Arising from the ashes of 9/11, a new tower is scheduled for completion  in 2013.

The architecture of the Freedom Tower reveals some interesting surprises. For one thing, the main body of the tower is, unlike most office towers, not a rectangular prism. Instead, the structure is that of an antiprism. This animated sequence gives a 360° view of an antiprism.

A square antiprism can be unfolded to create two pyramids, as shown in this animated sequence.

This geometric property reveals a lot about the architecture of the Freedom Tower and how it serves as a memorial to the Twin Towers.

Math in the News: 8/29/11

In the current issue of Math in the News, we look at a simple method for developing a computer tracking system for hurricanes. Using Excel, we create a “random walk” simulation of a hurricane path.

The key idea is that a truly random walk simulation would not produce anything like a hurricane’s path. A controlled randomness is what is required and this allows us to introduce the notion of managing the random variables.

In order to end up with a path that goes in a northwesterly direction, the random number generator must favor moving up and to the left, rather than down and to the right. The latter are not, of course, excluded, but the preponderance of the movement is in the preferred direction. Furthermore, students can tweak the random variables to create a hurricane path that goes toward the Gulf of Mexico or, like Hurricane Irene, along the Eastern Seaboard.

Try this activity as a back-to-school introduction to (or refresher on) random number generation.

Coming in 2012: Media4Math's Library++

Coming in 2012, Media4Math is pleased to announce the release of its online media libraries for Algebra, Geometry, and Graphing Calculators. Called Library++, this collection of multimedia resources will include lesson plans, interactive activities, video, animations, simulations, and assessment.

Media4Math's Algebra Library

The Algebra Library will launch in January 2012 and will include a complete set of multimedia resources to support a full-year algebra curriculum. This will be an ideal instructional and tutorial library that will literally bring algebra to life. Classroom teachers, homeschool educators, and resource centers will all benefit from the vast resources in this library.

TI-Nspire CX Library

Launching the spring of 2012, the TI-Nspire CX Library will include a complete library of interactive lessons that use the new TI-Nspire CX graphing calculator. No other media resource will come close to providing curriculum-focused support for integrating the Nspire CX. This library also offers support for a full-year algebra course.

Media4Math's Geometry Library

Finally, launching in the fall of 2012 is the Geometry Library, which is a complete multimedia resource for a full-year geometry course.

The Library++ Multimedia Solution will come at a single subscription price, depending on whether the end user is a student, teacher, school, or district. Our pricing will amaze you.

Get a preview of these libraries by clicking here. Each Library has its own tab that includes preview content.

Also, please register at our Library++ site to stay up-to-date on the launch and other pre-release news.

This first set deals with linear functions.

This next video deals with mapping a liner function to a quadratic.

This next video deals with mapping a liner function to a cubic function.

This next video deals with mapping a liner function to a polynomial function.

These videos deal with mapping a liner function to an exponential and a logarithmic function.

Math in the News: 8/15/11

In our next issue of Math in the News, we look at the new NFL Collective Bargaining Agreement (CBA). This is a follow-up to our 6/20/11 issue, which dealt with the previous CBA.

We focus on the new minimum salary requirements. This is important, since this affects the vast majority of NFL players. While there will always be super stars earning hundreds of millions of dollars, these are by far the outliers. The average NFL player, whose career is of finite length, needs a salary structure that ensures a livelihood that extends well beyond his NFL days.

This table summarizes the minimum salary, based on the number of completed seasons (CS) for a player and the starting year.

An analysis of this data allows for an exploration of the following math concepts:

• Discrete functions
• Step functions
• Linear regression
• Quadratic regression
• Data analysis

Math in the News: 8/8/11

In our next issue of Math in the News we look at federal spending. This is a timely topic, since the debt ceiling was recently increased and the levels of government spending are becoming worrisome as the national debt increases.

We look at data from the White House Office of Management and Budget (OMB), which has a wealth of data. These data sets are easily downloadable as Excel spreadsheets.

OMB data: Federal Spending from 2000-2010

We look at the dramatic increase in spending from 2000 to 2010 and ask, What was the year-to-year percent increase in spending? Students will likely estimate huge percentage increases, and the actual result will likely surprise them.

This activity is a great example of the power of compound interest.

Math in the News: 7/25/11

In our next issue of Math in the News, we investigate baseball stats, specifically we look at Derek Jeter’s recent accomplishment: joining the 3000+ hits club. His story is particularly interesting, since he is the first Yankee to do this. There were other Yankee players that eventually got to the 3000 plateau (e.g., Dave Winfield), but these weren’t Yankees at the time they reached 3000. In some ways, Jeter was lucky to be the first Yankee.

Jeter is only the second player in the 3000+ club to have hit a home run for his 3000th hit. Most members of the 3000+ club hit their 3000th hit as a single or double.

We investigate a number of data sets in different graph types. This activity would be great for back-to-school, as a way to review data analysis concepts.

The first allows students to add two integers and model the sum using tiles. As with all our Math Solvers, the user inputs values, in this case there is a drop-down menu for selecting each integer.

Once you select the two integers, then press the CALCULATE button to see a detailed solution–not just an answer. The goal is to provide instructional value, while solving a specific math problem.

The other Math Solver allows a student to solve equations of the form x + a = b, using Algebra Tiles. As with the first solver, select the parameters.

After selecting the parameters, press SOLVE to see a detailed solution.

Currently, these two solvers are limited to integer values from -10 to 10. Based on your feedback, we may modify these limits.

Please use these solvers and let us know what you think!