document.write( "Question 162179: I have to write each function in vertex form, and identity it's vertex.\r
\n" ); document.write( "\n" ); document.write( "g(x)=x^2-1/2x+1\r
\n" ); document.write( "\n" ); document.write( "could you please guide me on the step by step process on how to work this.\r
\n" ); document.write( "\n" ); document.write( "please help soon!\r
\n" ); document.write( "\n" ); document.write( "thx :) \n" ); document.write( "

Algebra.Com's Answer #119506 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Write in vertex form: $\"a%28x-h%29%5E2%2Bk+=+0\"$ :
\n" ); document.write( "You can convert to the vertex form of the equation by \"completing the square\"
\n" ); document.write( " $\"g%28x%29+=+x%5E2-%281%2F2%29x%2B1\"$ Set this function equal to zero.
\n" ); document.write( " $\"x%5E2-%281%2F2%29x%2B1+=+0\"$ Subtract 1 from both sides.
\n" ); document.write( " $\"x%5E2-%281%2F2%29x+=+-1\"$ Add the square of half the x-coefficient to both sides, that's $\"%28-1%2F4%29%5E2+=+1%2F16\"$ )
\n" ); document.write( " $\"%28x%5E2-%281%2F2%29x%2B+1%2F16%29+=+1%2F16-1\"$ Factor the trinomial on the left side.
\n" ); document.write( " $\"%28x-1%2F4%29%5E2+=+-15%2F16\"$ Add $\"15%2F16\"$ to both sides.
\n" ); document.write( " $\"%28x-1%2F4%29%5E2%2B15%2F16+=+0\"$ Compare with the standard vertex form:
\n" ); document.write( " $\"a%28x-h%29%5E2%2Bk+=+0\"$ The vertex is located at (h, k), so, $\"h+=+1%2F4\"$ and $\"k+=+15%2F16\"$
\n" ); document.write( "The vertex in your equation is located at: ( $\"1%2F4\"$ , $\"15%2F16\"$ )
\n" ); document.write( "Check the graph of the equation:
\n" ); document.write( " $\"graph%28400%2C400%2C-2%2C2%2C-2%2C2%2Cx%5E2-%281%2F2%29x%2B1%29\"$ \n" ); document.write( "

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