document.write( "Question 408202: Find the vertex, line of symmentry, and the max/min value of f(x)=1/5(x+2)^2+2, is the valuef(=2)=2 min or max and graph. I am having problems trying to solve this. \n" ); document.write( "

Algebra.Com's Answer #287641 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"f%28x%29+=+%281%2F5%29%2A%28x+%2B+2%29%5E2+%2B+2\"$
\n" ); document.write( "I can say $\"z+=+x+%2B+2\"$ , then
\n" ); document.write( " $\"f%28z%29+=+%281%2F5%29%2Az%5E2+%2B+2\"$
\n" ); document.write( "In an equation of the form
\n" ); document.write( " $\"f%28z%29+=+a%2Az%5E2+%2B+b%2Az+%2B+c\"$ , the z-coordinate of
\n" ); document.write( "the vertex is at $\"-b%2F%282a%29\"$ , but $\"b+=+0\"$
\n" ); document.write( "here, so (0,f(0)) is the vertex, and to find $\"y\"$
\n" ); document.write( " $\"f%280%29+=+%281%2F5%29%2A0%5E2+%2B+2\"$
\n" ); document.write( "The vertex is at (0,2)
\n" ); document.write( "Now I translate this to (x,f(x))
\n" ); document.write( " $\"z+=+x+%2B+2\"$
\n" ); document.write( " $\"0+=+x+%2B+2\"$
\n" ); document.write( " $\"x+=+-2\"$
\n" ); document.write( " $\"f%28-2%29+=+%281%2F5%29%2A%280%29%5E2+%2B+2\"$
\n" ); document.write( " $\"f%28-2%29+=+2\"$
\n" ); document.write( "(x,f(x)) = (-2,2)
\n" ); document.write( "The line of symmetry is $\"x+=+-2\"$
\n" ); document.write( "The graph is a min at $\"f%28x%29+=+2\"$
\n" ); document.write( "Here is the plot:
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+%281%2F5%29%2A%28x+%2B+2%29%5E2+%2B+2%29+\"$ \n" ); document.write( "

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