The Student Room Group

completing the square

express 4x squared + 2x -3 in the form of (2x+a)^2 -b ,

so i factorised the 2 out and i got 2(2x^2 + x) -3 , then i halfed the second coefficient and got 2( 2x+ 1/2) ^2 - 3.25

ok for that question i thought i could use the same method for this question, express 4x^2 + 8x- 21 in the form of a(x+p)^2 + q , i factorised the 4 and got 4( x^2+2x) -21, halved the second coffiecent and got 4(x^2 + 1)^2 -21 -1 , which is 4(x +1) ^2 -22, but that's wrong!! I don't kno how tho
Reply 1
Original post by ihatehannah
express 4x squared + 2x -3 in the form of (2x+a)^2 -b ,

so i factorised the 2 out and i got 2(2x^2 + x) -3 , then i halfed the second coefficient and got 2( 2x+ 1/2) ^2 - 3.25

ok for that question i thought i could use the same method for this question, express 4x^2 + 8x- 21 in the form of a(x+p)^2 + q , i factorised the 4 and got 4( x^2+2x) -21, halved the second coffiecent and got 4(x^2 + 1)^2 -21 -1 , which is 4(x +1) ^2 -22, but that's wrong!! I don't kno how tho


please post an image of the actual question
Original post by TeeEm
please post an image of the actual question


the acutal question is put 4x^2 + 8x -21 in the form a(x+p)^2 + q.
A picture will be more helpful because the lack of proper formatting has made the question in the OP difficult to read and understand.

Original post by ihatehannah
the acutal question is put 4x^2 + 8x -21 in the form a(x+p)^2 + q.
Reply 4
Original post by ihatehannah
the acutal question is put 4x^2 + 8x -21 in the form a(x+p)^2 + q.


well that is not the same you typed earlier ...

factorize the 4 out in square brackets
complete the square of the remaining expression inside the square bracket
multiply the 4 of the square bracket with the 2 terms inside the square bracket
Original post by TeeEm
well that is not the same you typed earlier ...

factorize the 4 out in square brackets
complete the square of the remaining expression inside the square bracket
multiply the 4 of the square bracket with the 2 terms inside the square bracket


so what exactly is the minimum value, -25?
Reply 6
Original post by ihatehannah
so what exactly is the minimum value, -25?


it is
Original post by TeeEm
it is


so that method can always be used to put 2x^2 -6x +3 in the form of (2x+a)^2 -b in exactly the same way?
(edited 8 years ago)
Reply 8
Original post by ihatehannah
so that method can always be used to put 2x^2 -6x +3 in the form of a(x+p)^2 + b in exactly the same way?


always

there is of course another which I teach but I never use

expand a(x+p)2 + b
2x2 -6x + 3 = ax2 + 2apx +(ap2 + b)
the compare coefficients of x2, then x then constant
Original post by TeeEm
always

there is of course another which I teach but I never use

expand a(x+p)2 + b
2x2 -6x + 3 = ax2 + 2apx +(ap2 + b)
the compare coefficients of x2, then x then constant


so is the minima value -3.5 ?
Reply 10
Original post by ihatehannah
so is the minima value -3.5 ?


i think it is -1.5
Original post by TeeEm
i think it is -1.5


ugh sorry i meant for 4x ^2 +2x -3 in the form of (2x+a)^2 - b, is the minima -3.5?
Reply 12
Original post by ihatehannah
ugh sorry i meant for 4x ^2 +2x -3 in the form of (2x+a)^2 - b, is the minima -3.5?


I think it is -3,25
Original post by TeeEm
I think it is -3,25


ughhhhh please explain how.
Reply 14
Original post by ihatehannah
ughhhhh please explain how.


4x2 - 2x -3 =
4[x2 - 1/2 x - 3/4] =
4[(x - 1/4 x)2 - 1/16 - 3/4] =
(x - 1/4 x)2 - 1/4 - 3 =
(x - 1/4 x)2 - 3.25

and now somebody else to take over please ...

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