document.write( "Question 639971: how do you graph y=x^2+6x+1 \n" ); document.write( "

Algebra.Com's Answer #402951 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+y+=+x%5E2+%2B+6x+%2B+1+\"$
\n" ); document.write( "The equation is in the form $\"+y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+\"$
\n" ); document.write( "First find the axis of symmetry.
\n" ); document.write( "That's a vertical line at
\n" ); document.write( " $\"+x+=+-b+%2F+%282a%29+\"$ and $\"+y+=+0+\"$
\n" ); document.write( " $\"+x+=+-6+%2F+%28+2%2A1+%29+=+-3+\"$
\n" ); document.write( "Draw this line, then find the point on the line
\n" ); document.write( "where the minimum is, ( -3,y[min] )
\n" ); document.write( " $\"+y%5Bmin%5D+=+%28-3%29%5E2+%2B+6%2A%28-3%29+%2B+1+\"$
\n" ); document.write( " $\"+y%5Bmin%5D+=+9+-+18+%2B+1+\"$
\n" ); document.write( " $\"+y%5Bmin%5D+=+-8+\"$
\n" ); document.write( "So the minimum is at (-3,-8) on the axis of symmetry
\n" ); document.write( "--------------
\n" ); document.write( "Now find the y-intercept at (0,y)
\n" ); document.write( " $\"+y+=+0%5E2+%2B+6%2A0+%2B+1+\"$
\n" ); document.write( " $\"+y+=+1+\"$
\n" ); document.write( "The y-intercept is at (0,1)
\n" ); document.write( "---------------
\n" ); document.write( "You can plug any values you want into $\"x\"$ and
\n" ); document.write( "get the value of $\"y\"$
\n" ); document.write( "I'll say $\"+x+=+-6+\"$
\n" ); document.write( " $\"+y+=+%28-6%29%5E2+%2B+6%2A%28-6%29+%2B+1+\"$
\n" ); document.write( " $\"+y+=+36+-+36+%2B+1+\"$
\n" ); document.write( " $\"+y+=+1+\"$
\n" ); document.write( "So the point (-6,1) lies on the graph
\n" ); document.write( "---------------
\n" ); document.write( "Here's the plot:
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-10%2C+3%2C+-10%2C+10%2C+x%5E2+%2B+6x+%2B+1+%29+\"$ \n" ); document.write( "

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