The function is defined for real values of x. By writing it in completed-square form, find its range.

f(x)=x^2-6x-+10

Thank you!!

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- Oct 2nd 2009, 07:47 AMOasis1993Help completing the square.
The function is defined for real values of x. By writing it in completed-square form, find its range.

f(x)=x^2-6x-+10

Thank you!! - Oct 2nd 2009, 07:52 AMDefunkt
$\displaystyle x^2-6x+10 = x^2-6x+9+1 = (x-3)^2 +1$

can you follow? - Oct 2nd 2009, 08:00 AMpickslides
Hi there

To complete the square you should consider the following

$\displaystyle f(x)=x^2-6x-10$

You need to find a new constant term by taking the middle term, halving it then squaring it. This gives...

$\displaystyle f(x)=(x^2-6x+9)-10-9$

$\displaystyle f(x)=(x^2-6x+9)-19$

$\displaystyle f(x)=(x-3)^2-19$

Now the square is complete.

The notation in your original post is ambigous. Defunkt's example may be what you're looking for.