document.write( "Question 188748: \n" ); document.write( "

Algebra.Com's Answer #141564 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
# 2\r
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\n" ); document.write( "\n" ); document.write( "In order to graph $\"y=x%5E2-6x-7\"$ , we need to plot a few points.\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-6x-7\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28-1%29%5E2-6%28-1%29-7\"$ Plug in $\"x=-1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1-6%28-1%29-7\"$ Square -1 to get 1.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1%2B6-7\"$ Multiply -6 and -1 to get 6.\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 $\"x=-1\"$ , $\"y=0\"$ . So we have the point (-1,0).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-6x-7\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%280%29%5E2-6%280%29-7\"$ Plug in $\"x=0\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=0-6%280%29-7\"$ Square 0 to get 0.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=0%2B0-7\"$ Multiply -6 and 0 to get 0.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-7\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ , $\"y=-7\"$ . So we have the point (0,-7).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-6x-7\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%29%5E2-6%281%29-7\"$ Plug in $\"x=1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1-6%281%29-7\"$ Square 1 to get 1.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1-6-7\"$ Multiply -6 and 1 to get -6.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-12\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , $\"y=-12\"$ . So we have the point (1,-12).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-6x-7\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%282%29%5E2-6%282%29-7\"$ Plug in $\"x=2\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4-6%282%29-7\"$ Square 2 to get 4.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4-12-7\"$ Multiply -6 and 2 to get -12.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-15\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=2\"$ , $\"y=-15\"$ . So we have the point (2,-15).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-6x-7\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%283%29%5E2-6%283%29-7\"$ Plug in $\"x=3\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=9-6%283%29-7\"$ Square 3 to get 9.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=9-18-7\"$ Multiply -6 and 3 to get -18.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-16\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=3\"$ , $\"y=-16\"$ . So we have the point (3,-16).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-6x-7\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%284%29%5E2-6%284%29-7\"$ Plug in $\"x=4\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=16-6%284%29-7\"$ Square 4 to get 16.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=16-24-7\"$ Multiply -6 and 4 to get -24.\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=-15\"$ Combine like terms.\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So when $\"x=4\"$ , $\"y=-15\"$ . So we have the point (4,-15).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=5\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-6x-7\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%285%29%5E2-6%285%29-7\"$ Plug in $\"x=5\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=25-6%285%29-7\"$ Square 5 to get 25.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=25-30-7\"$ Multiply -6 and 5 to get -30.\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=-12\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=5\"$ , $\"y=-12\"$ . So we have the point (5,-12).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=6\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-6x-7\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%286%29%5E2-6%286%29-7\"$ Plug in $\"x=6\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=36-6%286%29-7\"$ Square 6 to get 36.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=36-36-7\"$ Multiply -6 and 6 to get -36.\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=-7\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=6\"$ , $\"y=-7\"$ . So we have the point (6,-7).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=7\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-6x-7\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%287%29%5E2-6%287%29-7\"$ Plug in $\"x=7\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=49-6%287%29-7\"$ Square 7 to get 49.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=49-42-7\"$ Multiply -6 and 7 to get -42.\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 $\"x=7\"$ , $\"y=0\"$ . So we have the point (7,0).\r
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\n" ); document.write( "\n" ); document.write( "Now let's make a table of the values we just found.\r
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Table of Values:

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document.write( "x y
-1 0
0 -7
1 -12
2 -15
3 -16
4 -15
5 -12
6 -7
7 0\r\n" );
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document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Now let's plot the points:\r
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\r
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\n" ); document.write( "\n" ); document.write( "Now draw a curve through all of the points to graph $\"y=x%5E2-6x-7\"$ :\r
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Graph of $\"y=x%5E2-6x-7\"$ \r
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\n" ); document.write( "\n" ); document.write( "# 2\r
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\n" ); document.write( "\n" ); document.write( "In order to graph $\"y=x%5E2-4x-5\"$ , we need to plot a few points.\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=-2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-4x-5\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28-2%29%5E2-4%28-2%29-5\"$ Plug in $\"x=-2\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4-4%28-2%29-5\"$ Square -2 to get 4.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4%2B8-5\"$ Multiply -4 and -2 to get 8.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=7\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=-2\"$ , $\"y=7\"$ . So we have the point (-2,7).\r
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\n" ); document.write( "\n" ); document.write( "----------------------------\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-4x-5\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28-1%29%5E2-4%28-1%29-5\"$ Plug in $\"x=-1\"$ .\r
\n" ); document.write( "
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\n" ); document.write( "\n" ); document.write( " $\"y=1-4%28-1%29-5\"$ Square -1 to get 1.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1%2B4-5\"$ 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
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So when $\"x=-1\"$ , $\"y=0\"$ . So we have the point (-1,0).\r
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\n" ); document.write( "\n" ); document.write( "----------------------------\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-4x-5\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%280%29%5E2-4%280%29-5\"$ Plug in $\"x=0\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=0-4%280%29-5\"$ Square 0 to get 0.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=0%2B0-5\"$ Multiply -4 and 0 to get 0.\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=-5\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=0\"$ , $\"y=-5\"$ . So we have the point (0,-5).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-4x-5\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%29%5E2-4%281%29-5\"$ Plug in $\"x=1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1-4%281%29-5\"$ Square 1 to get 1.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1-4-5\"$ Multiply -4 and 1 to get -4.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-8\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=1\"$ , $\"y=-8\"$ . So we have the point (1,-8).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-4x-5\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%282%29%5E2-4%282%29-5\"$ Plug in $\"x=2\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4-4%282%29-5\"$ Square 2 to get 4.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4-8-5\"$ Multiply -4 and 2 to get -8.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-9\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=2\"$ , $\"y=-9\"$ . So we have the point (2,-9).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-4x-5\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%283%29%5E2-4%283%29-5\"$ Plug in $\"x=3\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=9-4%283%29-5\"$ Square 3 to get 9.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=9-12-5\"$ Multiply -4 and 3 to get -12.\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=-8\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So when $\"x=3\"$ , $\"y=-8\"$ . So we have the point (3,-8).\r
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\n" ); document.write( "\n" ); document.write( "----------------------------\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=4\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-4x-5\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=%284%29%5E2-4%284%29-5\"$ Plug in $\"x=4\"$ .\r
\n" ); document.write( "
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\n" ); document.write( "\n" ); document.write( " $\"y=16-4%284%29-5\"$ Square 4 to get 16.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=16-16-5\"$ Multiply -4 and 4 to get -16.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=-5\"$ Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So when $\"x=4\"$ , $\"y=-5\"$ . So we have the point (4,-5).\r
\n" ); document.write( "
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\n" ); document.write( "\n" ); document.write( "----------------------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=5\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-4x-5\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=%285%29%5E2-4%285%29-5\"$ Plug in $\"x=5\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=25-4%285%29-5\"$ Square 5 to get 25.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=25-20-5\"$ Multiply -4 and 5 to get -20.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=0\"$ Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So when $\"x=5\"$ , $\"y=0\"$ . So we have the point (5,0).\r
\n" ); document.write( "
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\n" ); document.write( "\n" ); document.write( "----------------------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=6\"$ \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-4x-5\"$ Start with the given equation.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=%286%29%5E2-4%286%29-5\"$ Plug in $\"x=6\"$ .\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=36-4%286%29-5\"$ Square 6 to get 36.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=36-24-5\"$ Multiply -4 and 6 to get -24.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=7\"$ Combine like terms.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So when $\"x=6\"$ , $\"y=7\"$ . So we have the point (6,7).\r
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\n" ); document.write( "\n" ); document.write( "----------------------------\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now let's make a table of the values we just found.\r
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Table of Values:

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document.write( "x y
-2 7
-1 0
0 -5
1 -8
2 -9
3 -8
4 -5
5 0
6 7\r\n" );
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document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Now let's plot the points:\r
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\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now draw a curve through all of the points to graph $\"y=x%5E2-4x-5\"$ :\r
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\n" ); document.write( "\n" ); document.write( "

Graph of $\"y=x%5E2-4x-5\"$ \n" ); document.write( "

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