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# Express 4x^2-4x-3 in the form (ax-b)^2-c watch

1. Hi, quick help with a question: Express 4x^2-4x-3 in the form (ax-b)^2-c, where a, b and c are positive constants to be found.
2. (Original post by jamiee207)
Hi, quick help with a question: Express 4x^2-4x-3 in the form (ax-b)^2-c, where a, b and c are positive constants to be found.
What have you tried
3. I haven't really, I have no idea why I can't do it either, it's supposed to be trivial considering it's the first part on an early question in my homework.
4. (Original post by jamiee207)
Hi, quick help with a question: Express 4x^2-4x-3 in the form (ax-b)^2-c, where a, b and c are positive constants to be found.
What did you try?

As a hint,

4x^2-4x-3 = 4[x^2-x-3/4]
5. (Original post by jamiee207)
I haven't really, I have no idea why I can't do it either, it's supposed to be trivial considering it's the first part on an early question in my homework.
Well, what is your usual approach to questions on completing the square?
6. You need to complete the square.

Firstly, consider the 4x^2. What multiplied by itself gives you 4x^2? This answer will be the ax part of your answer.

Now, you need to consider the -4x. What number multiplied with your ax and added together gives you -4x? This will give you the -b part to your answer.

Finally using your (ax-b)^2 break the bracket and see what you need to add or take away to make -3. This will give your-c part.

It is a more complex version of completing the square.
7. (Original post by MathsGeek89)
You need to complete the square.

Firstly, consider the 4x^2. What multiplied by itself gives you 4x^2? This answer will be the ax part of your answer.

Now, you need to consider the -4x. What number multiplied with your ax and added together gives you -4x? This will give you the -b part to your answer.

Finally using your (ax-b)^2 break the bracket and see what you need to add or take away to make -3. This will give your-c part.

It is a more complex version of completing the square.
It's easier to factorise the 4 and then just do the usual completing the square technique on x^2 - x - 3/4. Then just multiply through by 4.
8. IMPORTANT NOTE : I am not sure of this answer
a=4 b=-4 c=-3

x= -b/2a
= 4/8 = 0.5
y = 4(0.5)^2-4(0.5)-3
= -4
change the sign of x
4{(x-0.5)^2-4}
9. (Original post by Mohamed Mehaya)
IMPORTANT NOTE : I am not sure of this answer
a=4 b=-4 c=-3

x= -b/2a
= 4/8 = 0.5
y = 4(0.5)^2-4(0.5)-3
= -4
change the sign of x
4{(x-0.5)^2-4}
There's no point learning maths if you're going to memorise silly rules/formulas to solve equations, that's not what maths is about. UNDERSTAND why completing the square works, don't memorise a formula to complete the square.
10. (Original post by Mohamed Mehaya)
IMPORTANT NOTE : I am not sure of this answer
a=4 b=-4 c=-3

x= -b/2a
= 4/8 = 0.5
y = 4(0.5)^2-4(0.5)-3
= -4
change the sign of x
4{(x-0.5)^2-4}
Nearly, -4 isn't multiplied by 4 though.

expanding

11. (Original post by Swayum)
There's no point learning maths if you're going to memorise silly rules/formulas to solve equations, that's not what maths is about. UNDERSTAND why completing the square works, don't memorise a formula to complete the square.
There's a silly formula for completing the square?

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Updated: October 11, 2013
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