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# quick p2 question watch

1. why does the graph X^2 - 4ax cross the x axis at 4a and -4a? what happens to the x value once you sq root it?
2. (Original post by Bebop)
why does the graph X^2 - 4ax cross the x axis at 4a and -4a? what happens to the x value once you sq root it?
It doesn't - y = x(x - 4a) so it crosses when y = 0 ie x = 0, or x = 4a
3. (Original post by Bebop)
why does the graph X^2 - 4ax cross the x axis at 4a and -4a?
what? when x = 0 y = 0
4. (Original post by Bebop)
why does the graph X^2 - 4ax cross the x axis at 4a and -4a? what happens to the x value once you sq root it?
thsi is from the last p2 paper isnt it?

i dislike this question intensely.

you need to be really sharp: what it says is that it is an even function and over the range x>=0 it follows that curve. however becuase it is even, it is reflected in the y axis. isntead of looking like a parabola it now looks like a w, with roots at -4a, 0 and 4a.
5. (Original post by kikzen)
thsi is from the last p2 paper isnt it?

i dislike this question intensely.

you need to be really sharp: what it says is that it is an even function and over the range x>=0 it follows that curve. however becuase it is even, it is reflected in the y axis. isntead of looking like a parabola it now looks like a w, with roots at -4a, 0 and 4a.
which paper?
6. (Original post by lgs98jonee)
which paper?
jan 04 i think
7. (Original post by kikzen)
jan 04 i think
yeah i think it's from that paper too.

but regardin a small part of the original question, when you sqrt a negative no, u get "imaginary" no's that are denoted as "i". It comes into further maths, so cna't explain any more about it as I'm only doing single but i kno basically what they are.
8. (Original post by Hoofbeat)
yeah i think it's from that paper too.

but regardin a small part of the original question, when you sqrt a negative no, u get "imaginary" no's that are denoted as "i". It comes into further maths, so cna't explain any more about it as I'm only doing single but i kno basically what they are.
imaginary numbers:
root(-1) we all know is impossible. but in pure 4 we simple replace root(-1) with j. Sometimes when you do this it will simplify the equation in question and then you will get a j^2 which is -1. this doesnt happen very often as pure 4 is written by to bacteria that lives in the corns on satans feet. You can better show 'complex' numbers on an argand diagram where the x axis shows the real numbers and the y axis is the complex numbers. you can then perform transformations on these numbers such as adding 2(pi) will get you back to where you are. adding (pi) will extend the line into the adjacent quadrant etc.... i'm bad at pure 4 so some of this maybe wrong. correct me if it is!!!
9. Well if you have two circles that do not touch, then their roots are imaginary. But because xi/yi is a real number, you can still find the gradient of the line passing through the two "imaginary" points where the circles touch. Also when you add them, they become real so you can find the midpoint of two circles (where they meet), even though the places they touch don't actually exist.

Same with lines, such as y = x^2 + 1. The roots are +/- i, or +/- (root -1), but if you find the gradient of the line passing through these points,

m = (y2 - y1)/(x2 - x1) = (0-0)/(i-i) = 0. So the line is flat, even though the two points is passes through are imaginary.

That's how I understand it. Please correct me if I'm wrong.

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