document.write( "Question 117705: convert quadratic polynomial y(x)=x^2-6x+7 into vertex form [completeting full sqaure];find Xv,Yv, y-intercept, x-intercept and graph it. \n" ); document.write( "

Algebra.Com's Answer #85698 by josmiceli(19441) $\"\"$ $\"About$

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$\"y%28x%29+=+x%5E2+-+6x+%2B+7\"$
\n" ); document.write( "Find roots
\n" ); document.write( " $\"x%5E2+-+6x+%2B+7+=+0\"$
\n" ); document.write( " $\"x%5E2+-+6x+=+-7\"$
\n" ); document.write( "complete the square by taking half of the $\"-6\"$ , square it,
\n" ); document.write( "then add it to both sides
\n" ); document.write( " $\"x%5E2+-+6x+%2B+9+=+-7+%2B+9\"$
\n" ); document.write( " $\"%28x+-+3%29%5E2+=+2\"$
\n" ); document.write( " $\"x+-+3+=+0+%2B-sqrt%282%29\"$
\n" ); document.write( " $\"x+=+3+%2B+sqrt%282%29\"$
\n" ); document.write( " $\"x+=+3+-+sqrt%282%29\"$
\n" ); document.write( "The roots (x-intercepts) are at (3 + $\"sqrt%282%29\"$ , 0) and (3 - $\"sqrt%282%29\"$ ,0)
\n" ); document.write( "The vertex is exactly between them at (3, y). What is $\"y\"$ ?
\n" ); document.write( " $\"y%28x%29+=+x%5E2+-+6x+%2B+7\"$ make $\"x=3\"$
\n" ); document.write( " $\"y%283%29+=+3%5E2+-+6%2A3+%2B+7\"$
\n" ); document.write( " $\"y%283%29+=+9+-+18+%2B+7\"$
\n" ); document.write( " $\"y%283%29+=+-2\"$
\n" ); document.write( "So, the vertex is at (3,-2)
\n" ); document.write( "Lastly, where is the y-intercept? It is where $\"x=0\"$
\n" ); document.write( " $\"y%28x%29+=+x%5E2+-+6x+%2B+7\"$
\n" ); document.write( " $\"y%280%29+=+0%5E2+-+6%2A0+%2B+7\"$
\n" ); document.write( " $\"y%280%29+=+7\"$
\n" ); document.write( "The y-intercept is at (0,7)
\n" ); document.write( "Here's the graph
\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2+-+6x+%2B+7%29+\"$ \n" ); document.write( "

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