Jaynny
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Express 12x^2 - 6x + 5 in the form p(x-q)^2 + r
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VeryAverage
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This uses completing the square. The answer is 12(x - 0.25)^2 + 4.25.
So, the formula for changing it to this from a quadratic:
Quadratic: ax^2 + bx + c
Completed Square: a(x+ (b/2a))^2 + ................

Deriving the formula helps understand it better though!
There are sites you can use for more help, such as this one: https://www.mathsisfun.com/algebra/c...ng-square.html
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marceline666
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Completing the square

To make x^2 easier to work with, put everything in brackets
12(x^2 - 1/2 x + 5/12)

Half the x value and put in brackets as such
12[ (x-1/4)^2 ... ]

Add the rest, and subtract (1/4)^2 so you dont lose your original value
12[ (x-1/4)^2 -1/16 + 5/12 ]

then.....
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VeryAverage
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(Original post by marceline666)
12[ (x-1/4)^2 +17/48 ]
12(x-1/4)^2 + 5/4
Watch out, just noticed this

(17/48) x 12 = 204/48
204/48 = 17/4
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DangledTeaspoon
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marceline666
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(Original post by VeryAverage)
Watch out, just noticed this

(17/48) x 12 = 204/48
204/48 = 17/4
oops my bad, shouldnt have used a phone calculator
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simon0
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(Original post by DangledTeaspoon)
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Are you sure about this?
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DangledTeaspoon
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(Original post by simon0)
Are you sure about this?
Yea
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simon0
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(Original post by DangledTeaspoon)
Yea
From image in post 5:
TOP/ORIGINAL EQUATION:
 f(x) = 12 x^{2} -6x + 5.

So:  f(0) = 5.

EQUATION AT END:
 f(x) = 6 \Big( x - \frac{1}{2} \Big) ^{2} - \frac{7}{12}.

So:  f(0) = \frac{11}{12}.

-----------------------------------------------------------------------
The two equations are not equivalent.
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DangledTeaspoon
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(Original post by simon0)
From image in post 5:
TOP/ORIGINAL EQUATION:
 f(x) = 12 x^{2} -6x + 5.

So:  f(0) = 5.

EQUATION AT END:
 f(x) = 6 \Big( x - \frac{1}{2} \Big) ^{2} - \frac{7}{12}.

So:  f(0) = \frac{11}{12}.

-----------------------------------------------------------------------
The two equations are not equivalent.
I don’t know what all that means I thought it was just completing the square
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simon0
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(Original post by DangledTeaspoon)
I don’t know what all that means I thought it was just completing the square
Completing the square transforms one equation an equivalent one (with the end result being in a particular form).

So the output of the initial equation should be the same as the output of the last equation (in your script).

The expression after completing the square should be:

 \displaystyle 12 \left( x - \frac{1}{4} \right) ^{2} + \frac{17}{4}.
Last edited by simon0; 1 week ago
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wild_card_2005
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(Original post by Jaynny)
Express 12x^2 - 6x + 5 in the form p(x-q)^2 + r
Hey guys! It is so easy. Just u need to know how it works: how to complete the square: I learnt it on by Maths Daniel Dallas on Youtube - he is able to explain lots of dope concepts in Maths in very good way. Sometimes I amayzed why then people attend their School Maths classes
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