document.write( "Question 651391: How do you graph Y = x2 -6x +8? \n" ); document.write( "

Algebra.Com's Answer #407645 by MathLover1(20850) $\"\"$ $\"About$

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$\"y+=+x%5E2+-6x+%2B8\"$ \r
\n" ); document.write( "\n" ); document.write( "A parabola is of the general form $\"y+=+ax%5E2+%2B+bx+%2B+c\"$ , and you have that.\r
\n" ); document.write( "\n" ); document.write( "If $\"a\"$ is $\"positive\"$ the parabola $\"goes\"$ $\"+up\"$ (looks like a smiley face), if $\"a\"$ is $\"negative\"$ the parabola $\"goes\"$ $\"+down\"$ (looks like a sad face).\r
\n" ); document.write( "\n" ); document.write( "It is $\"very\"$ $\"+important\"$ to note that for your question, you have the opposite $\"y=x\"$ , instead of $\"x=y\"$ , you goes up. \r
\n" ); document.write( "\n" ); document.write( "In case of $\"x=y\"$ will be on $\"its\"$ $\"+side\"$ , and when this occurs, a positive $\"a\"$ value means it will go to the $\"right\"$ , so it will look like a letter $\"c\"$ .\r
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\n" ); document.write( "\n" ); document.write( "first, you can do is to find the vertex using $\"+-b%2F+2a\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+-b%2F+2a=-%28-6%29%2F2%2A1=6%2F2=3\"$ ...this is $\"x\"$ value...plug it in $\"y+=+x%5E2+-6x+%2B8\"$ and find $\"y\"$ value\r
\n" ); document.write( "\n" ); document.write( " $\"y+=+3%5E2+-6%2A3+%2B8\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y+=+9+-18+%2B8\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y+=+17+-18+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y+=+-1+\"$ \r
\n" ); document.write( "\n" ); document.write( "so, the vertex is at the point ( $\"3\"$ , $\"-1\"$ )\r
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\n" ); document.write( "\n" ); document.write( "In this example you can factor to find the $\"roots\"$ , the possible values for $\"x\"$ in our general form, when $\"y+=+0\"$ . \r
\n" ); document.write( "\n" ); document.write( "So,
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\n" ); document.write( " $\"y+=+x%5E2+-6x+%2B8\"$ ........substitute $\"-6x\"$ with $\"-2x+-4x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y+=+x%5E2+-2x+-4x+%2B8\"$ ...group\r
\n" ); document.write( "\n" ); document.write( " $\"y+=+%28x%5E2+-2x%29+-%284x+-8%29\"$ ...factor out $\"x\"$ from first group and $\"4\"$ from second group\r
\n" ); document.write( "\n" ); document.write( " $\"y=+x%28x+-2%29+-4%28x+-2%29\"$ ...set $\"y=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"0=+%28x+-4%29%28x+-2%29\"$ \r
\n" ); document.write( "\n" ); document.write( "if $\"%28x+-4%29=0\"$ ..->... $\"x=4\"$ \r
\n" ); document.write( "\n" ); document.write( "if $\"%28x+-2%29=0\"$ ..->... $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( "So the parabola passes through the $\"x-axis\"$ on the graph at $\"4\"$ and $\"2\"$ . As parabola are symmetrical, the $\"axis\"$ of $\"symmetry\"$ is halfway between these, ie $\"x+=3\"$ . \r
\n" ); document.write( "\n" ); document.write( "So sub this value into the original equation to find the lowest point of the parabola.\r
\n" ); document.write( "\n" ); document.write( " $\"y+=+x%5E2+-6x+%2B8\"$ ...now set $\"x=0\"$ and solve for $\"x\"$ to find $\"y-intercept\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y+=+0%5E2+-6%2A0+%2B8\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y+=+8\"$ ...so, there is $\"y-intercept\"$ at the point ( $\"0\"$ , $\"8\"$ )\r
\n" ); document.write( "\n" ); document.write( "you can also take few other positive and negative values for $\"x\"$ , calculate $\"y\"$ and plot that points too, and you are ready to draw a graph
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\n" ); document.write( "\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-6%2C+15%2C+-10%2C+15%2Cx%5E2+-2x+-4x+%2B8%29+\"$ \r
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