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Can a person use a quadratic formula to isolate the square in the process of completing...

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monique06 | (Level 3) Valedictorian

Posted May 31, 2013 at 2:20 PM via web

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Can a person use a quadratic formula to isolate the square in the process of completing the square?

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crmhaske | College Teacher | (Level 3) Associate Educator

Posted May 31, 2013 at 7:52 PM (Answer #1)

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The quadratic formula is arrived at by completing the square; therefore, theoretically one could use it to isolate the square through some simple rearranging:

`x=(-b+-sqrt(b^2-4ac))/(2a)`

`x+b/(2a)=+-sqrt(b^2-4ac)/(2a)`

`(x+b/(2a))^2=(b^2-4ac)/(4a^2)`

Therefore, the square is b/(2a)

With some further rearranging, we can arrive at the quadratic in vertex form:

`(x+b/(2a))^2-b^2/(4a^2)+c/a=0`

`a(x+b/(2a))^2-b^2/(4a)+c=0`

Therefore:

`h=b/(2a)` and` k=(c-b^2/(4a))` , where (h,k) is the vertex of the parabola.

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