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December 3, 2006
Random Sample of UK Data
This is the file I promised you that has the random UK data. Just click on the link below. Mr. Miles found this before, and I've created an extra link to it from this web blog.
Remember to click on the link and choose 'Save As' and then save it in a directory in your account.
Bouncing ball simulator
This is a simulator I wrote using PHP which allows you to create a gif of a bouncing ball with modifiable parameters. Below is a sample. If you want to try it out yourself, check out my programming blog.
December 1, 2006
Class Summary 1/12/06
In today's class Mr. Wees taught us how to complete the square in order to re-arrange a quadratic equation and the different forms to write a quadratic equation.
The general form is usually the one you start off with and it is written:
[tex]ax^2+bx+c=0[/tex]
The factored form is generally used to solve for y, and it looks like this:
[tex]a(x-r_1)(x-r_2)=y[/tex]
The standard form is the one most commonly used to graph.
[tex]a(x+k)^2+h=y[/tex]
The standard form is obtained by factoring the first two terms of the general form by adding x to half of b and squaring it in brackets. For example, we used:
[tex]x^2+6x+8=0[/tex]
6:3=2 so [tex](x+3)^2[/tex]
On the side we solved [tex](x+3)^2[/tex] and got [tex]x^2+6x+9[/tex], so we completed the square by adding 1 on both sides of the equation so that c would be 9 instead of 8 :
[tex]x^2+6x+8=0[/tex]
[tex]+1=+1[/tex]
[tex]x^2+6x+9=1[/tex]
This way the equation was equal. Then we moved the +1 to the other side of the equation by subtracting 1 on both sides, and got the final equation in standard form:
[tex](x+3)^2-1=0[/tex]
Then we tried to write another quadratic equation in standard form were a was not equal to 1. We started off with an equation in factored form, so we had to change it to general form first:
[tex](2x+1)(x+3)=0[/tex]
The general form is [tex]2x^2+6x+1x+3=0[/tex], and we simplified it to [tex]2x^2+7x+3=0[/tex]
The first step was so add [tex]x^2[/tex] to half of the 7 and multiply by 2:
[tex]2(x^2+3.5x)+3=0[/tex]
We factorised the numbers in brackets on the side:
[tex]x^2+3.5x=(x+1.75)^2-3.06259[/tex]
We plugged this in the formula, multiplying by a, which is 2:
[tex]2((x+1.75)-3.0625)+3=0[/tex]
[tex]=2(x+1.75)^2-6.125+3=0[/tex]
[tex]=2(x+1.75)^2-3.125=0[/tex]This is the standard form.
At the end of the lesson we were supposed to get a worksheet to practice with standard form, but we didn't have enough time.
The next person is...eleker!
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