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Completing the square

what does completing the square actually tell you?

i know can be used to
find the minimum point of a quadratic
to derive the quadratic formula
do c1 questions which require this skill

what uses does it have?
Reply 1
Avatar for B_9710
B_9710
18
Can be used to solve quadratics more conveniently.
Manipulate expressions in integrands to make things easier to integrate.
Original post by thefatone
what does completing the square actually tell you?

i know can be used to
find the minimum point of a quadratic
to derive the quadratic formula
do c1 questions which require this skill

what uses does it have?


Pretty much what you said. It's sort of an easier way to factorise a quadratic.
Reply 3
Avatar for thefatone
thefatone
OP
6
Original post by john_jomcy98
Pretty much what you said. It's sort of an easier way to factorise a quadratic.


i know but it doesn't give the fully factorised version/using the forumla
It's used in FP3 to turn things in to a different form that is easier to integrate
Reply 5
Avatar for Zacken
Zacken
22
Original post by thefatone
Completing the square


I know that this isn't the directly related to the question but you might enjoy reading this post.
Original post by Zacken
I know that this isn't the directly related to the question but you might enjoy reading this post.


can you have quadratics with imaginary numbers?
Reply 7
Avatar for thefatone
thefatone
OP
6
Original post by Student403
It's used in FP3 to turn things in to a different form that is easier to integrate


Original post by B_9710
Can be used to solve quadratics more conveniently.
Manipulate expressions in integrands to make things easier to integrate.



that's new.... da how i wish i did further maths now >.>

Original post by Zacken
I know that this isn't the directly related to the question but you might enjoy reading this post.


will do...
Reply 8
Avatar for Zacken
Zacken
22
Original post by Youngmetro
can you have quadratics with imaginary numbers?


Yes. Do you mean as coefficients or factoring them over the complex plane? If it's the former: definitely, if it's the latter: still definitely. The complex number field acts as the algebraic extension or closure of the real number field, so you can definitely factorise a quadratic with real coefficients into two linear factors.
Original post by thefatone
what does completing the square actually tell you?

i know can be used to
find the minimum point of a quadratic
to derive the quadratic formula
do c1 questions which require this skill

what uses does it have?


You have asked two different questions here, but I'll give an answer to the first: completing the square tells you that, given a rectangle, you can always find a square with a smaller square removed, with the same area as the rectangle. For example:

x2+6x=x(x+6)x^2+6x = x(x+6) is the area of a rectangle of sides x,x+6x, x+6. But by competing the square, we have x(x+6)=(x+3)2−32x(x+6) = (x+3)^2-3^2 which is the area of a square of side x+3x+3 with a smaller square, area 323^2 removed.

You can see a graphical representation of this here: http://www.thestudentroom.co.uk/showpost.php?p=51716679&postcount=5
Reply 10
Avatar for Zacken
Zacken
22
Original post by atsruser

You can see a graphical representation of this here:


Perhaps more complicated than needs be, but meh:

Original post by Zacken
Perhaps more complicated than needs be, but meh:


That's neat, but not very easy to follow, I think.
Reply 12
Avatar for Zacken
Zacken
22
Original post by atsruser
That's neat, but not very easy to follow, I think.


Yeah, I agree - I much preferred your simpler and more concise example.
Reply 13
Avatar for thefatone
thefatone
OP
6
Original post by atsruser
You have asked two different questions here, but I'll give an answer to the first: completing the square tells you that, given a rectangle, you can always find a square with a smaller square removed, with the same area as the rectangle. For example:

x2+6x=x(x+6)x^2+6x = x(x+6) is the area of a rectangle of sides x,x+6x, x+6. But by competing the square, we have x(x+6)=(x+3)2−32x(x+6) = (x+3)^2-3^2 which is the area of a square of side x+3x+3 with a smaller square, area 323^2 removed.

You can see a graphical representation of this here: http://www.thestudentroom.co.uk/showpost.php?p=51716679&postcount=5


Original post by Zacken
Perhaps more complicated than needs be, but meh:



thanks both of you, now i can understand why it's called completing the square xD

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