# Finding domain and range of a function without graphing it

• Sep 9th 2010, 03:38 PM
jsaroya
Finding domain and range of a function without graphing it
Hi, how can I find the domain and range of this function without graphing:

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

I know domain is x is any real number..How do i find the range
• Sep 9th 2010, 03:43 PM
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Quote:

Originally Posted by jsaroya
Hi, how can I find the domain and range of this function without graphing:

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

I know domain is x is any real number..How do i find the range

Find the vertex (where the parabola changes direction).

If you are in Pre-Algebra and Algebra as your post location suggests, you can find the vertex by putting the equation in the form suggested here

Parabola - Wikipedia, the free encyclopedia

If you happen to be in Calculus and just filed this post in Pre-Algebra and Algebra by mistake, you can find the global minimum by taking the derivative and setting it to 0.
• Sep 9th 2010, 03:45 PM
jsaroya
Yes I am in Pre-algebra. So I convert it into vertex form using something like the completing the square method?
• Sep 9th 2010, 05:40 PM
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You are right, completing the square is the standard way to solve this using elementary methods, unless you have memorized the formula x = -b/(2a). Here is a link that's rather easier to follow than Wikipedia and shows worked examples.

Vertex of a Parabola

(Scroll down a bit to where it discusses general equations of the form x = ax^2 + bx + c.)

If you have any questions feel free to post again.
• Sep 10th 2010, 07:22 AM
jsaroya
Thank you!