document.write( "Question 1130541: Find the range of
\n" ); document.write( "f(x) = −x2 − 6x − 7. \n" ); document.write( "

Algebra.Com's Answer #747224 by MathLover1(20849) $\"\"$ $\"About$

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\n" ); document.write( " $\"f%28x%29+=+-x%5E2+-6x+-7\"$ \r
\n" ); document.write( "\n" ); document.write( "here you have parabola that opens downward; so, it has a maximum at vertex\r
\n" ); document.write( "\n" ); document.write( "range will be all below $\"y\"$ coordinate of the vertex\r
\n" ); document.write( "\n" ); document.write( "write your equation in vertex form:\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=+-%28x%5E2+%2B6x%29+-7\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=+-1%2A%28x%5E2+%2B6x%2Bb%5E2%29-1%2A%28-b%5E2%29+-7\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=+-%28x%5E2+%2B6x%2B3%5E2%29%2B3%5E2+-7\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=+-%28x%2B3%29%5E2%29%2B9+-7\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=+-%28x%2B3%29%5E2%29%2B2\"$ => $\"k=2\"$ => $\"y\"$ coordinate of the vertex\r
\n" ); document.write( "\n" ); document.write( "then, range is:\r
\n" ); document.write( "\n" ); document.write( "{ $\"f%28x%29\"$ element $\"R\"$ : $\"f%28x%29+%3C=2\"$ }\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-%28x%2B3%29%5E2%2B2%29+\"$ \r
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