algerbraaa easy question :)

**johnsmith666** · January 5th 2010, 09:36 AM

express x^2 - 5x + 1/4 in the form (x-a)^2 - b

**Archie Meade** · January 5th 2010, 09:41 AM

$(x-a)^2=x^2-2ax+a^2$

$2a=5$

$a=\frac{5}{2}$

$(x-a)^2-b=x^2-2ax+a^2-b$

$a^2-b=\frac{1}{4}$

$\frac{25}{4}-b=\frac{1}{4}$

**johnsmith666** · January 5th 2010, 09:44 AM

sorry im confuseddd :s i needed the answer in the form (x-a)^2 - b.

**Archie Meade** · January 5th 2010, 09:51 AM

$b=\frac{25}{4}-\frac{1}{4}=\frac{24}{4}$

Now you have both 'a' and 'b'.

Practice with that.

**Archie Meade** · January 5th 2010, 09:55 AM

"a" and "b" are both constants,
they have no 'x'.

When you multiply out $(x-a)^2$ you get

$(x-a)(x-a)=x(x-a)-a(x-a)=x^2-ax-ax+a^2=x^2-2ax+a^2$

This means $-5=-2a$

So you've got the value of 'a' now.
Use this value of 'a' to find 'b'.

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