document.write( "Question 148855: Graph the polynomial function:
\n" ); document.write( "f(x)=x^3+4x^2+x-6\r
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Algebra.Com's Answer #109196 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "Jump to Table\r
\n" ); document.write( "\n" ); document.write( "Jump to Graph\r
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\n" ); document.write( "\n" ); document.write( "In order to graph $\"y=x%5E3%2B4x%5E2%2Bx-6\"$ , we need to plot some points.\r
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\n" ); document.write( "\n" ); document.write( "Let's find y when $\"x=-3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E3%2B4x%5E2%2Bx-6\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28-3%29%5E3%2B4%28-3%29%5E2%2B-3-6\"$ Plug in $\"x=-3\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1%28-27%29%2B4%28-3%29%5E2-3-6\"$ Cube $\"-3\"$ to get $\"-27\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1%28-27%29%2B4%289%29-3-6\"$ Square $\"-3\"$ to get $\"9\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-27%2B4%289%29-3-6\"$ Multiply $\"1\"$ and $\"-27\"$ to get $\"-27\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-27%2B36-3-6\"$ Multiply $\"4\"$ and $\"9\"$ to get $\"36\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=0\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-3\"$ , then $\"y=0\"$ .\r
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\n" ); document.write( "\n" ); document.write( "So we have the point

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\n" ); document.write( "\n" ); document.write( "Let's find y when $\"x=-2\"$ :\r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E3%2B4x%5E2%2Bx-6\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28-2%29%5E3%2B4%28-2%29%5E2%2B-2-6\"$ Plug in $\"x=-2\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1%28-8%29%2B4%28-2%29%5E2-2-6\"$ Cube $\"-2\"$ to get $\"-8\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1%28-8%29%2B4%284%29-2-6\"$ Square $\"-2\"$ to get $\"4\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-8%2B4%284%29-2-6\"$ Multiply $\"1\"$ and $\"-8\"$ to get $\"-8\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-8%2B16-2-6\"$ Multiply $\"4\"$ and $\"4\"$ to get $\"16\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=0\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-2\"$ , then $\"y=0\"$ .\r
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\n" ); document.write( "\n" ); document.write( "So we have the point

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\n" ); document.write( "\n" ); document.write( "Let's find y when $\"x=-1\"$ :\r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E3%2B4x%5E2%2Bx-6\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28-1%29%5E3%2B4%28-1%29%5E2%2B-1-6\"$ Plug in $\"x=-1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1%28-1%29%2B4%28-1%29%5E2-1-6\"$ Cube $\"-1\"$ to get $\"-1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1%28-1%29%2B4%281%29-1-6\"$ Square $\"-1\"$ to get $\"1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-1%2B4%281%29-1-6\"$ Multiply $\"1\"$ and $\"-1\"$ to get $\"-1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-1%2B4-1-6\"$ Multiply $\"4\"$ and $\"1\"$ to get $\"4\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-4\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-1\"$ , then $\"y=-4\"$ .\r
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\n" ); document.write( "\n" ); document.write( "So we have the point

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\n" ); document.write( "\n" ); document.write( "Let's find y when $\"x=0\"$ :\r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E3%2B4x%5E2%2Bx-6\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%280%29%5E3%2B4%280%29%5E2%2B0-6\"$ Plug in $\"x=0\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1%280%29%2B4%280%29%5E2%2B0-6\"$ Cube $\"0\"$ to get $\"0\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1%280%29%2B4%280%29%2B0-6\"$ Square $\"0\"$ to get $\"0\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=0%2B4%280%29%2B0-6\"$ Multiply $\"1\"$ and $\"0\"$ to get $\"0\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=0%2B0%2B0-6\"$ Multiply $\"4\"$ and $\"0\"$ to get $\"0\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-6\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ , then $\"y=-6\"$ .\r
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\n" ); document.write( "\n" ); document.write( "So we have the point

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\n" ); document.write( "\n" ); document.write( "Let's find y when $\"x=1\"$ :\r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E3%2B4x%5E2%2Bx-6\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%29%5E3%2B4%281%29%5E2%2B1-6\"$ Plug in $\"x=1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1%281%29%2B4%281%29%5E2%2B1-6\"$ Cube $\"1\"$ to get $\"1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1%281%29%2B4%281%29%2B1-6\"$ Square $\"1\"$ to get $\"1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1%2B4%281%29%2B1-6\"$ Multiply $\"1\"$ and $\"1\"$ to get $\"1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1%2B4%2B1-6\"$ Multiply $\"4\"$ and $\"1\"$ to get $\"4\"$ .\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=0\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , then $\"y=0\"$ .\r
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\n" ); document.write( "\n" ); document.write( "So we have the point

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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E3%2B4x%5E2%2Bx-6\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%282%29%5E3%2B4%282%29%5E2%2B2-6\"$ Plug in $\"x=2\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1%288%29%2B4%282%29%5E2%2B2-6\"$ Cube $\"2\"$ to get $\"8\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1%288%29%2B4%284%29%2B2-6\"$ Square $\"2\"$ to get $\"4\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=8%2B4%284%29%2B2-6\"$ Multiply $\"1\"$ and $\"8\"$ to get $\"8\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=8%2B16%2B2-6\"$ Multiply $\"4\"$ and $\"4\"$ to get $\"16\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=20\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=2\"$ , then $\"y=20\"$ .\r
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Table of Values:

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document.write( "x y
-3 0
-2 0
-1 -4
0 -6
1 0
2 20\r\n" );
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Graph:

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\n" ); document.write( "\n" ); document.write( "Now draw a curve through all of the points to graph $\"y=x%5E3%2B4x%5E2%2Bx-6\"$ :\r
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Graph of $\"y=x%5E3%2B4x%5E2%2Bx-6\"$ \n" ); document.write( "

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