document.write( "Question 128757: Can you please help me graph this equation?
\n" ); document.write( "y=-x^2+6x+5 \n" ); document.write( "

Algebra.Com's Answer #94189 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
In order to graph $\"f%28x%29=-1x%5E2%2B6x%2B5\"$ , we need to plot some points. To do that, we need to plug in some x values to get some y values\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-1x%5E2%2B6x%2B5\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=-1%28-2%29%5E2%2B6%28-2%29%2B5\"$ Plug in $\"x=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=-1%2A4%2B6%2A-2%2B5\"$ Raise -2 to the 2nd power to get 4\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=-4%2B6%2A-2%2B5\"$ Multiply -1 and 4 to get -4\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=-4%2B-12%2B5\"$ Multiply 6 and -2 to get -12\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=-16%2B5\"$ Add -4 and -12 to get -16\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-2%29=-11\"$ Add -16 and 5 to get -11\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-2\"$ , we have $\"y=-11\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 1st point is (-2,-11)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-1x%5E2%2B6x%2B5\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=-1%28-1%29%5E2%2B6%28-1%29%2B5\"$ Plug in $\"x=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=-1%2A1%2B6%2A-1%2B5\"$ Raise -1 to the 2nd power to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=-1%2B6%2A-1%2B5\"$ Multiply -1 and 1 to get -1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=-1%2B-6%2B5\"$ Multiply 6 and -1 to get -6\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=-7%2B5\"$ Add -1 and -6 to get -7\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28-1%29=-2\"$ Add -7 and 5 to get -2\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-1\"$ , we have $\"y=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 2nd point is (-1,-2)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-1x%5E2%2B6x%2B5\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=-1%280%29%5E2%2B6%280%29%2B5\"$ Plug in $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=-1%2A0%2B6%2A0%2B5\"$ Raise 0 to the 2nd power to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=0%2B6%2A0%2B5\"$ Multiply -1 and 0 to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=0%2B0%2B5\"$ Multiply 6 and 0 to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=0%2B5\"$ Add 0 and 0 to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%280%29=5\"$ Add 0 and 5 to get 5\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ , we have $\"y=5\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 3rd point is (0,5)\r
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\n" ); document.write( "\n" ); document.write( "-------------- Let's find another point --------------\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-1x%5E2%2B6x%2B5\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-1%281%29%5E2%2B6%281%29%2B5\"$ Plug in $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-1%2A1%2B6%2A1%2B5\"$ Raise 1 to the 2nd power to get 1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-1%2B6%2A1%2B5\"$ Multiply -1 and 1 to get -1\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=-1%2B6%2B5\"$ Multiply 6 and 1 to get 6\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=5%2B5\"$ Add -1 and 6 to get 5\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%29=10\"$ Add 5 and 5 to get 10\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , we have $\"y=10\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 4th point is (1,10)\r
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\n" ); document.write( "\n" ); document.write( "-------------- Let's find another point --------------\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-1x%5E2%2B6x%2B5\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=-1%282%29%5E2%2B6%282%29%2B5\"$ Plug in $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=-1%2A4%2B6%2A2%2B5\"$ Raise 2 to the 2nd power to get 4\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=-4%2B6%2A2%2B5\"$ Multiply -1 and 4 to get -4\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=-4%2B12%2B5\"$ Multiply 6 and 2 to get 12\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=8%2B5\"$ Add -4 and 12 to get 8\r
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\n" ); document.write( "\n" ); document.write( " $\"f%282%29=13\"$ Add 8 and 5 to get 13\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=2\"$ , we have $\"y=13\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 5th point is (2,13)\r
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\n" ); document.write( "\n" ); document.write( "-------------- Let's find another point --------------\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-1x%5E2%2B6x%2B5\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=-1%283%29%5E2%2B6%283%29%2B5\"$ Plug in $\"x=3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=-1%2A9%2B6%2A3%2B5\"$ Raise 3 to the 2nd power to get 9\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=-9%2B6%2A3%2B5\"$ Multiply -1 and 9 to get -9\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=-9%2B18%2B5\"$ Multiply 6 and 3 to get 18\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=9%2B5\"$ Add -9 and 18 to get 9\r
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\n" ); document.write( "\n" ); document.write( " $\"f%283%29=14\"$ Add 9 and 5 to get 14\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=3\"$ , we have $\"y=14\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 6th point is (3,14)\r
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\n" ); document.write( "\n" ); document.write( "-------------- Let's find another point --------------\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-1x%5E2%2B6x%2B5\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=-1%284%29%5E2%2B6%284%29%2B5\"$ Plug in $\"x=4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=-1%2A16%2B6%2A4%2B5\"$ Raise 4 to the 2nd power to get 16\r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=-16%2B6%2A4%2B5\"$ Multiply -1 and 16 to get -16\r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=-16%2B24%2B5\"$ Multiply 6 and 4 to get 24\r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=8%2B5\"$ Add -16 and 24 to get 8\r
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\n" ); document.write( "\n" ); document.write( " $\"f%284%29=13\"$ Add 8 and 5 to get 13\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=4\"$ , we have $\"y=13\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 7th point is (4,13)\r
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\n" ); document.write( "\n" ); document.write( "-------------- Let's find another point --------------\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-1x%5E2%2B6x%2B5\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%285%29=-1%285%29%5E2%2B6%285%29%2B5\"$ Plug in $\"x=5\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%285%29=-1%2A25%2B6%2A5%2B5\"$ Raise 5 to the 2nd power to get 25\r
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\n" ); document.write( "\n" ); document.write( " $\"f%285%29=-25%2B6%2A5%2B5\"$ Multiply -1 and 25 to get -25\r
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\n" ); document.write( "\n" ); document.write( " $\"f%285%29=-25%2B30%2B5\"$ Multiply 6 and 5 to get 30\r
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\n" ); document.write( "\n" ); document.write( " $\"f%285%29=5%2B5\"$ Add -25 and 30 to get 5\r
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\n" ); document.write( "\n" ); document.write( " $\"f%285%29=10\"$ Add 5 and 5 to get 10\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=5\"$ , we have $\"y=10\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 8th point is (5,10)\r
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\n" ); document.write( "\n" ); document.write( "-------------- Let's find another point --------------\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-1x%5E2%2B6x%2B5\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%286%29=-1%286%29%5E2%2B6%286%29%2B5\"$ Plug in $\"x=6\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%286%29=-1%2A36%2B6%2A6%2B5\"$ Raise 6 to the 2nd power to get 36\r
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\n" ); document.write( "\n" ); document.write( " $\"f%286%29=-36%2B6%2A6%2B5\"$ Multiply -1 and 36 to get -36\r
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\n" ); document.write( "\n" ); document.write( " $\"f%286%29=-36%2B36%2B5\"$ Multiply 6 and 6 to get 36\r
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\n" ); document.write( "\n" ); document.write( " $\"f%286%29=0%2B5\"$ Add -36 and 36 to get 0\r
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\n" ); document.write( "\n" ); document.write( " $\"f%286%29=5\"$ Add 0 and 5 to get 5\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=6\"$ , we have $\"y=5\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 9th point is (6,5)\r
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\n" ); document.write( "\n" ); document.write( "-------------- Let's find another point --------------\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-1x%5E2%2B6x%2B5\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%287%29=-1%287%29%5E2%2B6%287%29%2B5\"$ Plug in $\"x=7\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%287%29=-1%2A49%2B6%2A7%2B5\"$ Raise 7 to the 2nd power to get 49\r
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\n" ); document.write( "\n" ); document.write( " $\"f%287%29=-49%2B6%2A7%2B5\"$ Multiply -1 and 49 to get -49\r
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\n" ); document.write( "\n" ); document.write( " $\"f%287%29=-49%2B42%2B5\"$ Multiply 6 and 7 to get 42\r
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\n" ); document.write( "\n" ); document.write( " $\"f%287%29=-7%2B5\"$ Add -49 and 42 to get -7\r
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\n" ); document.write( "\n" ); document.write( " $\"f%287%29=-2\"$ Add -7 and 5 to get -2\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=7\"$ , we have $\"y=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 10th point is (7,-2)\r
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\n" ); document.write( "\n" ); document.write( "-------------- Let's find another point --------------\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=-1x%5E2%2B6x%2B5\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%288%29=-1%288%29%5E2%2B6%288%29%2B5\"$ Plug in $\"x=8\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%288%29=-1%2A64%2B6%2A8%2B5\"$ Raise 8 to the 2nd power to get 64\r
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\n" ); document.write( "\n" ); document.write( " $\"f%288%29=-64%2B6%2A8%2B5\"$ Multiply -1 and 64 to get -64\r
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\n" ); document.write( "\n" ); document.write( " $\"f%288%29=-64%2B48%2B5\"$ Multiply 6 and 8 to get 48\r
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\n" ); document.write( "\n" ); document.write( " $\"f%288%29=-16%2B5\"$ Add -64 and 48 to get -16\r
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\n" ); document.write( "\n" ); document.write( " $\"f%288%29=-11\"$ Add -16 and 5 to get -11\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=8\"$ , we have $\"y=-11\"$ \r
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\n" ); document.write( "\n" ); document.write( "So our 11th point is (8,-11)\r
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\n" ); document.write( "\n" ); document.write( "Now lets make a table of the values we have calculated\r
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document.write( " x y
 -2 -11
 -1 -2
 0 5
 1 10
 2 13
 3 14
 4 13
 5 10
 6 5
 7 -2
 8 -11\r\n" );
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Now plot the points\r
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\r
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\n" ); document.write( "\n" ); document.write( "Now connect the points to graph $\"y=-1x%5E2%2B6x%2B5\"$ (note: the more points you plot, the easier it is to draw the graph)\r
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