document.write( "Question 153191: I am trying to graph y=-x^2 -8x +9, I am not sure how to solve and graph \n" ); document.write( "
Algebra.Com's Answer #112715 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
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Jump to Table\r
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\n" ); document.write( "\n" ); document.write( "In order to graph \"y=-x%5E2-8x%2B9\", we need to plot some points.\r
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\n" ); document.write( "\n" ); document.write( "Let's find y when \"x=-9\"\r
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\n" ); document.write( "\n" ); document.write( "\"y=-x%5E2-8x%2B9\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"y=-%28-9%29%5E2-8%28-9%29%2B9\" Plug in \"x=-9\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-1%2881%29-8%28-9%29%2B9\" Square \"-9\" to get \"81\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-81-8%28-9%29%2B9\" Multiply \"-1\" and \"81\" to get \"-81\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-81%2B72%2B9\" Multiply \"-8\" and \"-9\" to get \"72\".\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=-9\", then \"y=0\".\r
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\n" ); document.write( "\n" ); document.write( "So we have the point .\r
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\n" ); document.write( "\n" ); document.write( "Let's find y when \"x=-8\":\r
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\n" ); document.write( "\n" ); document.write( "\"y=-x%5E2-8x%2B9\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"y=-%28-8%29%5E2-8%28-8%29%2B9\" Plug in \"x=-8\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-1%2864%29-8%28-8%29%2B9\" Square \"-8\" to get \"64\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-64-8%28-8%29%2B9\" Multiply \"-1\" and \"64\" to get \"-64\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-64%2B64%2B9\" Multiply \"-8\" and \"-8\" to get \"64\".\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=-8\", then \"y=9\".\r
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\n" ); document.write( "\n" ); document.write( "So we have the point .\r
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\n" ); document.write( "\n" ); document.write( "Let's find y when \"x=-7\":\r
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\n" ); document.write( "\n" ); document.write( "\"y=-x%5E2-8x%2B9\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"y=-%28-7%29%5E2-8%28-7%29%2B9\" Plug in \"x=-7\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-1%2849%29-8%28-7%29%2B9\" Square \"-7\" to get \"49\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-49-8%28-7%29%2B9\" Multiply \"-1\" and \"49\" to get \"-49\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-49%2B56%2B9\" Multiply \"-8\" and \"-7\" to get \"56\".\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=-7\", then \"y=16\".\r
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\n" ); document.write( "\n" ); document.write( "So we have the point .\r
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\n" ); document.write( "\n" ); document.write( "Let's find y when \"x=-6\":\r
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\n" ); document.write( "\n" ); document.write( "\"y=-x%5E2-8x%2B9\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"y=-%28-6%29%5E2-8%28-6%29%2B9\" Plug in \"x=-6\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-1%2836%29-8%28-6%29%2B9\" Square \"-6\" to get \"36\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-36-8%28-6%29%2B9\" Multiply \"-1\" and \"36\" to get \"-36\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-36%2B48%2B9\" Multiply \"-8\" and \"-6\" to get \"48\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=21\" Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So when \"x=-6\", then \"y=21\".\r
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\n" ); document.write( "\n" ); document.write( "So we have the point .\r
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\n" ); document.write( "\n" ); document.write( "Let's find y when \"x=-5\":\r
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\n" ); document.write( "\n" ); document.write( "\"y=-x%5E2-8x%2B9\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"y=-%28-5%29%5E2-8%28-5%29%2B9\" Plug in \"x=-5\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-1%2825%29-8%28-5%29%2B9\" Square \"-5\" to get \"25\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-25-8%28-5%29%2B9\" Multiply \"-1\" and \"25\" to get \"-25\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-25%2B40%2B9\" Multiply \"-8\" and \"-5\" to get \"40\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=24\" Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So when \"x=-5\", then \"y=24\".\r
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\n" ); document.write( "\n" ); document.write( "So we have the point .\r
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\n" ); document.write( "\n" ); document.write( "Let's find y when \"x=-4\":\r
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\n" ); document.write( "\n" ); document.write( "\"y=-x%5E2-8x%2B9\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"y=-%28-4%29%5E2-8%28-4%29%2B9\" Plug in \"x=-4\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-1%2816%29-8%28-4%29%2B9\" Square \"-4\" to get \"16\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-16-8%28-4%29%2B9\" Multiply \"-1\" and \"16\" to get \"-16\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-16%2B32%2B9\" Multiply \"-8\" and \"-4\" to get \"32\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=25\" Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So when \"x=-4\", then \"y=25\".\r
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\n" ); document.write( "\n" ); document.write( "So we have the point .\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%5E2-8x%2B9\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"y=-%28-3%29%5E2-8%28-3%29%2B9\" Plug in \"x=-3\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-1%289%29-8%28-3%29%2B9\" Square \"-3\" to get \"9\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-9-8%28-3%29%2B9\" Multiply \"-1\" and \"9\" to get \"-9\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-9%2B24%2B9\" Multiply \"-8\" and \"-3\" to get \"24\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=24\" Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So when \"x=-3\", then \"y=24\".\r
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\n" ); document.write( "\n" ); document.write( "So we have the point .\r
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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%5E2-8x%2B9\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"y=-%28-2%29%5E2-8%28-2%29%2B9\" Plug in \"x=-2\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-1%284%29-8%28-2%29%2B9\" Square \"-2\" to get \"4\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-4-8%28-2%29%2B9\" Multiply \"-1\" and \"4\" to get \"-4\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-4%2B16%2B9\" Multiply \"-8\" and \"-2\" to get \"16\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=21\" Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So when \"x=-2\", then \"y=21\".\r
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\n" ); document.write( "\n" ); document.write( "So we have the point .\r
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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%5E2-8x%2B9\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"y=-%28-1%29%5E2-8%28-1%29%2B9\" Plug in \"x=-1\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-1%281%29-8%28-1%29%2B9\" Square \"-1\" to get \"1\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-1-8%28-1%29%2B9\" Multiply \"-1\" and \"1\" to get \"-1\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-1%2B8%2B9\" Multiply \"-8\" and \"-1\" to get \"8\".\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=-1\", then \"y=16\".\r
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\n" ); document.write( "\n" ); document.write( "So we have the point .\r
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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%5E2-8x%2B9\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"y=-%280%29%5E2-8%280%29%2B9\" Plug in \"x=0\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-1%280%29-8%280%29%2B9\" Square \"0\" to get \"0\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=0-8%280%29%2B9\" Multiply \"-1\" and \"0\" to get \"0\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=0%2B0%2B9\" Multiply \"-8\" and \"0\" to get \"0\".\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=0\", then \"y=9\".\r
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\n" ); document.write( "\n" ); document.write( "So we have the point .\r
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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%5E2-8x%2B9\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"y=-%281%29%5E2-8%281%29%2B9\" Plug in \"x=1\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-1%281%29-8%281%29%2B9\" Square \"1\" to get \"1\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-1-8%281%29%2B9\" Multiply \"-1\" and \"1\" to get \"-1\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-1-8%2B9\" Multiply \"-8\" and \"1\" to get \"-8\".\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\", then \"y=0\".\r
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\n" ); document.write( "\n" ); document.write( "So we have the point .\r
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Jump to Top of Page\r
\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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xy
-90
-89
-716
-621
-524
-425
-324
-221
-116
09
10
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\r
\n" ); document.write( "\n" ); document.write( "Now let's plot the points:\r
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Jump to Top of Page\r
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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%5E2-8x%2B9\":\r
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\n" ); document.write( "\n" ); document.write( " Graph of \"y=-x%5E2-8x%2B9\"
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