document.write( "Question 130759: Using $\"f%28x%29=%281%2F2%29%28x%2B4%29%5E2%2B7\"$ , find the vertex, the equation of the line of symmetry, and the max/min value of f(x). \n" ); document.write( "

Algebra.Com's Answer #95470 by jim_thompson5910(35256) $\"\"$ $\"About$

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$\"f%28x%29=%281%2F2%29%28x%2B4%29%5E2%2B7\"$ Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=%281%2F2%29%28x-%28-4%29%29%5E2%2B7\"$ Rewrite $\"x%2B4\"$ as $\"x-%28-4%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now the equation is in vertex form $\"y=a%28x-h%29%5E2%2Bk\"$ where \"a\" is the stretch/compression factor and (h,k) is the vertex. So this means that $\"a=1%2F2\"$ , $\"h=-4\"$ , and $\"k=7\"$ \r
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\n" ); document.write( "\n" ); document.write( "So the vertex is (-4,7)\r
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\n" ); document.write( "\n" ); document.write( "Now the equation of the line of symmetry is in the general form $\"x=h\"$ . So the equation of the line of symmetry is $\"x=-4\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now since the vertex is where the max/min occurs, this means that the max/min of f(x) is the y-coordinate of the vertex. So the max/min of f(x) is 7 \n" ); document.write( "

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