SOLUTION: Find the domain and the range of the quadratic function whose minimum value is 15 at x=−5, Would I just plug in 15 for x?

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Question 1120589: Find the domain and the range of the quadratic function whose minimum value is 15 at x=−5, Would I just plug in 15 for x?
Found 2 solutions by solver91311, ikleyn:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


The domain of a function is the set of all numbers for which the function is defined. For all polynomial functions, a classification that includes all quadratic functions, the domain is all real numbers, i.e.:




The range of a function is the set of all possible values for a function evaluated at all possible values of the domain. For all polynomial functions of even degree, a classification that includes all quadratic functions, there is an absolute minimum value (for those polynomial functions where the lead coefficient is positive) or an absolute maximum value (lead coefficient negative). In the case of your example, -5 is the absolute minimum value, and the function does not have a maximum value. That means the range is the set of all real values that are greater than or equal to -5. So for :




John

My calculator said it, I believe it, that settles it
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
In this problem, the domain is the set of all real numbers (the entire number line).


The range is the set of all real numbers, greater or equal to 15. 


In the interval form, the range is the set  [,).



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