Question 1024785
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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[max]}}}.

Find the maximum of f(x).

It is y-coordinate of its vertex.

To find it, you can complete the square:

{{{-x^2-10x}}} = {{{-(x^2 + 10x)}}} = {{{-((x+5)^2 - 25)}}} = {{{-(x+5)^2}}} + {{{25}}}.

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

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