Simple question - need help :(
I am re-sitting this test I done in January as I only just got an A and would like to have got a bit better, and as you can see below, i've forgot everything! Anyway, here it is;
Ok, this question is from this paper; http://eiewebvip.edexcel.org.uk/Reports/Confidential%20Documents/0506/6663_01_que_20050623.pdf
It's 3a.
x^2 – 8x – 29 = (x + a)^2 + b
Find a and b.
It seems so simple yet i can't see how to do it, an explaination would be great.
Ok, this question is from this paper; http://eiewebvip.edexcel.org.uk/Reports/Confidential%20Documents/0506/6663_01_que_20050623.pdf
It's 3a.
x^2 – 8x – 29 = (x + a)^2 + b
Find a and b.
It seems so simple yet i can't see how to do it, an explaination would be great.
Original post by vc94
Called completing the square:
x^2 + 2bx = (x + b)^2 - b^2
x^2 + 2bx = (x + b)^2 - b^2
Apply this general result to x^2 - 8x
Original post by LiamRigby
Still confused as that makes no sense or seems to have no relevance to my question :/ ?
No it's very relevent. Answering that question is called completing the square.
x^2 + 2yx = (x + y)^2 - y^2
This the general rule you apply.
http://en.wikipedia.org/wiki/Completing_the_square
have you done completing the square?
like the person above said so
x^2 + 2bx - a = (x + b)^2 - b^2 - a
it works best when the coefficient of x is an even number so you can halve it easily, which it is with your question (-8x), remember that as it is a negative number you are halving you need to keep the negative number in the brackets.
If you expand the brackets afterwards just to see why it works you can see that you need to get rid of the extra b^2 by subtracting it, and don't forget to leave your value of a in there (-29).
Hope this helps
like the person above said so
x^2 + 2bx - a = (x + b)^2 - b^2 - a
it works best when the coefficient of x is an even number so you can halve it easily, which it is with your question (-8x), remember that as it is a negative number you are halving you need to keep the negative number in the brackets.
If you expand the brackets afterwards just to see why it works you can see that you need to get rid of the extra b^2 by subtracting it, and don't forget to leave your value of a in there (-29).
Hope this helps
Do you know how to complete the square?
Spoiler
or you could just expand the bracket on the right-hand side and compare and contrast with the left-hand side
Ahhh, a lot has been explained and I now get it! ;D
However, if I went straight from this line:
x^2-8x-29 = (x-a)^2+b to...
(x-4)^2-16-29 = (x-a)^2+b
would I get marked down for not showing the formula? As I never actually used the formula, I used Supernova's way;
However, if I went straight from this line:
x^2-8x-29 = (x-a)^2+b to...
(x-4)^2-16-29 = (x-a)^2+b
would I get marked down for not showing the formula? As I never actually used the formula, I used Supernova's way;
You halve the coefficient of X and then take away that squared, so (x-4)^2 -16 -29 = 0
(x-4)^2 -45
(x-4)^2 -45
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