document.write( "Question 581166: Find the vertex, maximum or minimum value, range, and intervals where it increases and decreases. f(x)=x^2 - 12 - 1 \n" ); document.write( "

Algebra.Com's Answer #371487 by dfrazzetto(283) $\"\"$ $\"About$

You can put this solution on YOUR website!
f(x)=x^2 - 12x - 1, I am assuming this is what you meant to write:\r
\n" ); document.write( "\n" ); document.write( "vertex form, complete the square:\r
\n" ); document.write( "\n" ); document.write( "f(x) = x^2 -12x + 36 -1 -36\r
\n" ); document.write( "\n" ); document.write( "f(x) = (x - 6)^2 -37\r
\n" ); document.write( "\n" ); document.write( "Vertex = (6,-37)\r
\n" ); document.write( "\n" ); document.write( "upward facing parabola, max=infinity, minimum @ vertex (6,-37)\r
\n" ); document.write( "\n" ); document.write( "f'(x) = 2x -12 = 0
\n" ); document.write( "x=6\r
\n" ); document.write( "\n" ); document.write( "range = [-37, infinity)\r
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\n" ); document.write( "\n" ); document.write( " $\"+graph%28+900%2C+900%2C+-10%2C+20%2C+-40%2C+50%2C+x%5E2+-+12x+-+1%29+\"$ \r
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