Awesome page, really great stuff!
I just noticed a few things:
Small typo for "iseems":
In this case it iseems easiest to set them equal to each other:
And the solve by substitution method for 3x3 under the section "Now replace "z" with "3 - y" in the other equation:" the 3-y is not aligned correctly. 3-y is not on one line but the y goes underneath.
"A "root" (or "zero") is where the function crosses the x-axis "
Maybe this should be reworded to 'A "root" (or "zero") is a value where the function equals 0' because the function doesn't have to cross the x-axis, but it could be tangent with it. And then show a example: f(3) = 3^2 + 4(3) - 21 = 0
Yup, I was just curious. Thanks for your feedback. I think I figured it out, I'm teaching myself this stuff. I had a pretty crummy math education. Teachers weren't that great. Anyways, from your reply on my other question "How to derive other equations from the general conic section equation?" I'm assuming that Bxy = 0, Cy2 = 0, and Ey = 0 for the general conic section equation: Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 and what's left is a quadratic. From that I can get the discriminant.
I've just read the Conic Sections page and at the bottom it says that the general equation can be used to create equations for the circle, ellipse, parabola and hyperbola. How can I create those equations? BTW, I've search all of Google and couldn't find anything.
How can I derived the conic section discriminant from the general equation Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0
The book I'm reading says that it's taken from A,B,C. I don't see how Ax^2 + Bxy + Cy^2 can be turned into b^2-4ac. I know that Ax^2 + Bx + C can be used to get the discriminant from learning about quadratics, but like I said the book says it uses A,B,C. My best guess is that they meant it's derived from Ax^2 + Dx + F. I'm not sure but I think I'm interpreting the text wrong. Can someone please clear this up for me? Thanks.
I saw this problem on sosmath.com - http://www.sosmath.com/algebra/pfrac/pfrac.html
x^3 - 4x^2 + 5
and it's suppose to factor out to (x+1)(x^2-5x+5) and I've been sitting here trying to get it to that form but I only end up with (x^2+5)(x-4). Can someone please shed some light to how this can be factored out to (x+1)(x^2-5x+5). Thanks!
So, I've survived all my math classes from elementary school through college (BS), but I've gotten through without understanding why I'm learning what I was being taught. I felt lost and still feel lost. I'm finding it difficult seeing the whole picture. I'm looking for a chart, map or list of some kind that shows the major areas of math and how they are related to each other. I think if I have something visual to look at I will have a better sense of how everything fits together. Also, it would be helpful if it described where that area of mathematics is applied. Do you know where I can find this? Or can you help me out and make one. Thanks! John