SOLUTION: Find the domain and range f(x)= -x^2-10x

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Question 1024785: Find the domain and range
f(x)= -x^2-10x

Answer by ikleyn(52800) About Me  (Show Source):
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Find the domain and range
f(x)= -x^2-10x
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The domain is (-infinity, infinity), the set of all real numbers.

The range is from -infinity to f%5Bmax%5D.

Find the maximum of f(x).

It is y-coordinate of its vertex.

To find it, you can complete the square:

-x%5E2-10x = -%28x%5E2+%2B+10x%29 = -%28%28x%2B5%29%5E2+-+25%29 = -%28x%2B5%29%5E2 + 25.

The maximum is at x = -5, and it is equal to 25.

Hence, the range is (-infinity, 25).