Thread: Finding domain and range of a function without graphing it

1. 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

2. 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.

3. Yes I am in Pre-algebra. So I convert it into vertex form using something like the completing the square method?

4. 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.

5. Thank you!