Homework Help: Square root of a function

1. The problem statement, all variables and given/known data

I have the function H^2 + 12756H and I want to find the domain and range of it's square root algebraically.


2. Relevant equations


3. The attempt at a solution

I understand y= √(H^2 + 12756H) is undefined if H^2 + 12756H < 0, however I dont get how to find its domain and range using algebra. Maybe someone can help me.

 

I understand how to find the domain and range of the root function by looking at the original graph, however my question is can it be done algebraically, if so how?

And no I dont believe you can solve for H with 0 = h^2 + 12756h algebraically only with quadratic formula. The point of this post is to find out the easiest way to solve this sort of thing for domain, and would it be finding x-intercepts and deriving your domain of the root from that ?