document.write( "Question 335943: use the quadratic formula to determine the x-intercepts (if any) of the following function. Then evaluate the function for several values of x, and use the resulting points to graph the function. Show your work; \r
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\n" ); document.write( "\n" ); document.write( "could someone please help me with this problem.\r
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Algebra.Com's Answer #240932 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
Finding the x-intercepts:\r
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\n" ); document.write( "\n" ); document.write( "Simply plug in \"f%28x%29=0\" to get \"0=x%5E2-2x-4\". The goal now is to solve for 'x'.\r
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\n" ); document.write( "\n" ); document.write( "Notice that the quadratic \"x%5E2-2x-4\" is in the form of \"Ax%5E2%2BBx%2BC\" where \"A=1\", \"B=-2\", and \"C=-4\"\r
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\n" ); document.write( "\n" ); document.write( "Let's use the quadratic formula to solve for \"x\":\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29\" Start with the quadratic formula\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%28-4%29+%29%29%2F%282%281%29%29\" Plug in \"A=1\", \"B=-2\", and \"C=-4\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%281%29%28-4%29+%29%29%2F%282%281%29%29\" Negate \"-2\" to get \"2\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%282+%2B-+sqrt%28+4-4%281%29%28-4%29+%29%29%2F%282%281%29%29\" Square \"-2\" to get \"4\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%282+%2B-+sqrt%28+4--16+%29%29%2F%282%281%29%29\" Multiply \"4%281%29%28-4%29\" to get \"-16\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%282+%2B-+sqrt%28+4%2B16+%29%29%2F%282%281%29%29\" Rewrite \"sqrt%284--16%29\" as \"sqrt%284%2B16%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%282+%2B-+sqrt%28+20+%29%29%2F%282%281%29%29\" Add \"4\" to \"16\" to get \"20\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%282+%2B-+sqrt%28+20+%29%29%2F%282%29\" Multiply \"2\" and \"1\" to get \"2\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%282+%2B-+2%2Asqrt%285%29%29%2F%282%29\" Simplify the square root (note: If you need help with simplifying square roots, check out this solver) \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%282%29%2F%282%29+%2B-+%282%2Asqrt%285%29%29%2F%282%29\" Break up the fraction. \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+1+%2B-+1%2Asqrt%285%29\" Reduce. \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+1%2B1%2Asqrt%285%29\" or \"x+=+1-1%2Asqrt%285%29\" Break up the expression. \r
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\n" ); document.write( "\n" ); document.write( "So the solutions are \"x+=+1%2B1%2Asqrt%285%29\" or \"x+=+1-1%2Asqrt%285%29\" \r
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\n" ); document.write( "\n" ); document.write( "which approximate to \"x=3.236\" or \"x=-1.236\" \r
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\n" ); document.write( "\n" ); document.write( "So the x-intercepts are roughly (3.236, 0) and (-1.236, 0)\r
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\n" ); document.write( "\n" ); document.write( "In order to graph \"y=x%5E2-2x-4\", we need to plot some points.\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%5E2-2x-4\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"y=%28-2%29%5E2-2%28-2%29-4\" Plug in \"x=-2\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=4-2%28-2%29-4\" Square \"-2\" to get \"4\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=4%2B4-4\" Multiply \"-2\" and \"-2\" 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=-2\", then \"y=4\".\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%5E2-2x-4\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"y=%28-1%29%5E2-2%28-1%29-4\" Plug in \"x=-1\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=1-2%28-1%29-4\" Square \"-1\" to get \"1\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=1%2B2-4\" Multiply \"-2\" and \"-1\" to get \"2\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-1\" Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So when \"x=-1\", then \"y=-1\".\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%5E2-2x-4\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"y=%280%29%5E2-2%280%29-4\" Plug in \"x=0\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=0-2%280%29-4\" Square \"0\" to get \"0\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=0%2B0-4\" Multiply \"-2\" and \"0\" to get \"0\".\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=0\", then \"y=-4\".\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%5E2-2x-4\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"y=%281%29%5E2-2%281%29-4\" Plug in \"x=1\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=1-2%281%29-4\" Square \"1\" to get \"1\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=1-2-4\" Multiply \"-2\" and \"1\" to get \"-2\".\r
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\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=1\", then \"y=-5\".\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%5E2-2x-4\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"y=%282%29%5E2-2%282%29-4\" Plug in \"x=2\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=4-2%282%29-4\" Square \"2\" to get \"4\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=4-4-4\" Multiply \"-2\" and \"2\" 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=2\", then \"y=-4\".\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%5E2-2x-4\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"y=%283%29%5E2-2%283%29-4\" Plug in \"x=3\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=9-2%283%29-4\" Square \"3\" to get \"9\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=9-6-4\" Multiply \"-2\" and \"3\" to get \"-6\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=-1\" Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So when \"x=3\", then \"y=-1\".\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%5E2-2x-4\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"y=%284%29%5E2-2%284%29-4\" Plug in \"x=4\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=16-2%284%29-4\" Square \"4\" to get \"16\".\r
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\n" ); document.write( "\n" ); document.write( "\"y=16-8-4\" Multiply \"-2\" and \"4\" to get \"-8\".\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=4\", then \"y=4\".\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( "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
-24
-1-1
0-4
1-5
2-4
3-1
44
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\n" ); document.write( "\n" ); document.write( "Now let's plot the points:\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%5E2-2x-4\":\r
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\n" ); document.write( "\n" ); document.write( " Graph of \"y=x%5E2-2x-4\"\r
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\n" ); document.write( "\n" ); document.write( "If you need more help, email me at jim_thompson5910@hotmail.com\r
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\n" ); document.write( "\n" ); document.write( "Also, feel free to check out my website. \r
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\n" ); document.write( "\n" ); document.write( "Jim
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