September 2011 - Page 9 of 11 - Math and Multimedia

Making Connection Between Distance and Absolute Value

September 7, 2011 GB High School Algebra, High School Mathematics

We have learned about the distance formula and we also have discussed how to get the distance between two points given their coordinates. In this post, we are going to explore a simpler concept: getting the distance between two points on the number line.

Suppose we want to get the distance between two p0ints on the number line whose coordinates are integers, we can just do it by counting. In the figure below, the distance from $0$ to $5$ is $5$ , and the distance from $5$ to $9$ is $4$ .

image via nctm illuminations

It is also obvious that we can get the distance by subtraction: $5-0=5$ and $9-5=4$ . It is clear that if we let $a$ be the larger integer, and $b$ be the smaller, then the distance can between the two integers is $a-b$ . It is also clear that this formula applies to non-integral coordinates. » Read more

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Record and Share your Presentation with Present.Me

September 6, 2011 GB Teaching Tools, Web 2.0 Technology

Present.Me is a new site that lets you record and share your PowerPoint presentation. What makes Present.Me unique is that the site lets you add a narrative to your presentation through a web cam and a microphone. Once done, you can publish your presentation and share them on the web.

Click the image to go to actual presentation

Present.Me has currently a free account that allows you to create ten 15-minute recordings per month. There is also a plus and max account for a fee.

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Understanding the Meaning of Discriminant

September 5, 2011 GB High School Algebra, High School Mathematics

In the Derivation of the Quadratic Formula, we have learned that the solutions to the quadratic equation $ax^2 + bx + c = 0$ , where $a \neq 0$ , is described by the equation

$x = \displaystyle\frac{-b \pm \sqrt{b^2-4ac}}{2a}$ .

Graphically, getting the solutions of $ax^2 + bx + c = 0$ is equivalent to getting the value of $x$ when $y=0$ of the function $f(x) = ax^2 + bx + c$ , $a \neq 0$ . This means that the quadratic formula above describes the root of the quadratic function $f$ .

From the equation, the $\pm$ indicates that the quadratic polynomial can have at most two roots, depending on the value of the expression under the radical sign. That is, the roots of the quadratic polyonomials are

$x = \displaystyle\frac{-b + \sqrt{b^2-4ac}}{2a}$

and

$x = \displaystyle\frac{-b - \sqrt{b^2-4ac}}{2a}$ .

The number of roots, however, will depend on the expression $b^2 - 4ac$ . Notice that if it is negative, there is no root (real root to be exact), since we cannot extract the square root of a negative number. Therefore, if $b^2 - 4ac < 0$ , then, there is no real root. » Read more

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