I wish I could step across and help with the quadratic equations, Heather. They aren't really that hard, if you can find the way that works for you. I learned them by ignoring the way the school was trying to teach them and found my own method that worked better for me.
A quadratic equation can be a scary looking thing when you know you don't get them. I know they had me bluffed for years. I mean - they're a mixture of three different terms that can't be combined any further: a squared pronumeral, a pronumeral with a factor multiplying it, and an integer.
Example - Xsquared - 3X - 4.
What worked for me was to just LOOK at it, and look at the numbers at the front.
Xsquared - it has a factor of 1, here. -3X has a factor of -3. and -4 - that could be 4 x 1 or 2 x 2, one of those numbers being negative.
Instead of drawing that silly cross thing, I just began to write the answer, two brackets. Because the first fragment of the problem was Xsquared, I knew that I needed to write:
(X - ?) (X - ?). I put "-" signs in, because all they need is a vertical line to turn them into "+" signs. They put the space in that I need, for the mathematical symbol.
Next I look at the second term - "-3X". When you multiply out a bracketed problem like this, you get two lots of X times a digit (here, shown above by "?"). First you get the first X being multiplied by the integer in the second brackets, then the second X being multiplied by the integer in the first brackets. Since they are both "X times integer" they add together easily. You might have X times 5 plus 3 times X - that comes to 5X + 3X which neatly adds to 8X. But that's not the answer to our example here.
So we have, for Xsquared - 3X - 4, the answer so far as (X - ?) (X - ?). Because the last term is minus, we know that one of these brackets HAS to be minus and one plus (because + times - gives a -factor; - times - gives a plus).
Now we go to the last term, or fragment of the quadratic: -4. What are the possible factors of -4? They are 2 x 2, or 4 x 1. One factor is +, the other is -. But which? For the answer, we look back at the second term. What factors multiply to make -4, but add to make -3?
Clearly it can't be 2 and 2. It has to be 1 and 4. So I write in the digits to replace the "?" and we now have (X - 1) (X - 4).
This is NOT yet the answer - we need to check the signs and multiply it through to make sure we've got the answer. But to add together to get get -3, we need the - in front of the 4, the + in front of the 1. That would give the answer: (X + 1) (X - 4).
To multiply it through: first you multiply everything in the second bracket (X - 4) by X, then you multiply it by +1. You then arrange it all so the like terms are all together and it looks neat. Does it work?
It should. X times X is X squared. Then it's X times 1, which is X. Then it's -4 times X, plus -4 x 1.
So you get Xsquared + 1X - 4X - 4. Right.
It's awkward trying to do this without using superscripts, but once you understand how it's supposed to work, and understand it in your own way, it should be easy. Sometimes you just have to find a different way that works for you.
If difficult child worked so hard, even if she didn't make a lot of progress - good for her!
Something I might suggest - we bought a cheap computer tuition CD ROM which was a summary of basic high school maths. It's like a revision book, only it's on computer. It cost us about A$60 at most and we've found it very helpful. Seriously - the sooner you can get on top of maths problems that are causing you trouble, the less ground you lose in your confidence. Sometimes we're looking for something to be more difficult than it really is, and can't believe it's so simple; there HAS to be a catch. It's how it's taught sometimes, the teacher approaching with fear and trepidation so the student is already thinking, "I'll never get this!"
A did this a few times at school - just ignored the way the teacher was doing it and read the textbook for myself, working out my own method.
The other option is to get someone to give her (or you) some coaching on how to do it. But if you can, see if you can find a simple (and cheap) computer disc first. Ours was from a mob called The Learning Company; I don't know if this helps.
Marg