document.write( "Question 76541: I don't know exactly how to get this form y=a(x-h)^2+k from the function y=x^2-6x+8. I don't know how to get this function into this particular form. \n" ); document.write( "

Algebra.Com's Answer #54896 by Earlsdon(6294) $\"\"$ $\"About$

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Convert:
\n" ); document.write( " $\"y+=+x%5E2-6x%2B8\"$ to:
\n" ); document.write( " $\"y+=+a%28x-k%29%5E2%2Bk\"$ from.
\n" ); document.write( "Use the process known as \"completing the square\"
\n" ); document.write( " $\"y+=+x%5E2-6x%2B8\"$ You want to make the constant term here equal to the square of half the x-coefficient (that's the -6).
\n" ); document.write( " $\"%28-6%2F2%29%5E2+=+9\"$
\n" ); document.write( "So you must add a 1 to the 8 to make the required 9. But to keep the same equation, you must also subtract 1 to compensate for the added 1.
\n" ); document.write( " $\"y+=+x%5E2-6x%2B8%2B1-1\"$ Now rearrange this as follows:
\n" ); document.write( " $\"y+=+%28x%5E2-6x%2B9%29-1\"$ Factor the parentheses.
\n" ); document.write( " $\"y+=+%28x-5%29%5E2-1\"$ ...and there you have it! Compare with:
\n" ); document.write( " $\"y+=+a%28x-h%29%5E2%2Bk\"$
\n" ); document.write( "Here: a = 1, h = 5, and k = -1 \n" ); document.write( "

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