document.write( "Question 118381: Sketch the graphs, using the given roots to determine the function and the turning point.
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\n" ); document.write( " a. x = -2, x=4
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Algebra.Com's Answer #86500 by jim_thompson5910(35256)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "\"x=-2\" or \"x=4\" Start with the given roots\r
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\n" ); document.write( "\n" ); document.write( "\"x%2B2=0\" or \"x-4=0\" Add 2 to both sides for the first root. Subtract 4 from both sides for the second root.\r
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\n" ); document.write( "\n" ); document.write( "\"%28x%2B2%29%28x-4%29=0\" Now use the zero product property in reverse. Remember the zero product property says that if \"A%2AB=0\" then \"A=0\" or \"B=0\"\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2-2x-8=0\" Now foil. note: Let me know if you need help with foiling.\r
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\n" ); document.write( "\n" ); document.write( "So the function with roots of \"x=-2\" or \"x=4\" is \"f%28x%29=x%5E2-2x-8\"\r
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\n" ); document.write( "\n" ); document.write( "Now to find the turning point, we need to find the x-coordinate of the turning point. To do that, simply use this formula: \"x=-b%2F2a\"\r
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\n" ); document.write( "\n" ); document.write( "So from \"f%28x%29=x%5E2-2x-8\" we can see that \"a=1\" and \"b=-2\". \r
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\n" ); document.write( "\n" ); document.write( "\"x=-%28-2%29%2F2%281%29\" Plug \"a=1\" and \"b=-2\" into the formula. \r
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\n" ); document.write( "\n" ); document.write( "\"x=-%28-2%29%2F2\" Multiply\r
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\n" ); document.write( "\n" ); document.write( "\"x=2%2F2\" Negate -2 to get 2\r
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\n" ); document.write( "\n" ); document.write( "\"x=1\" Reduce\r
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\n" ); document.write( "\n" ); document.write( "So the x-coordinate of the turning point is \"x=1\" \r
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\n" ); document.write( "\n" ); document.write( "Now we have to evaluate \"f%281%29\" to determine the y-coordinate of the turning point.\r
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\n" ); document.write( "\n" ); document.write( "\"f%28x%29=x%5E2-2x-8\" Start with the given function.\r
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\n" ); document.write( "\n" ); document.write( "\"f%281%29=%281%29%5E2-2%281%29-8\" Plug in \"x=1\". In other words, replace each x with 1.\r
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\n" ); document.write( "\n" ); document.write( "\"f%281%29=%281%29-2%281%29-8\" Evaluate \"%281%29%5E2\" to get 1.\r
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\n" ); document.write( "\n" ); document.write( "\"f%281%29=%281%29-2-8\" Multiply -2 and 1 to get -2\r
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\n" ); document.write( "\n" ); document.write( "\"f%281%29=-9\" Now combine like terms\r
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\n" ); document.write( "\n" ); document.write( "So the turning point is (1,-9) \r
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\n" ); document.write( "\n" ); document.write( "Notice if we graph \"f%28x%29=x%5E2-2x-8\", we can see that the roots are \"x=-2\" and \"x=4\". We can also see that the turning point is (1,-9). So this visually verifies our answer.\r
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\n" ); document.write( "\n" ); document.write( "\"+graph%28500%2C500%2C-10%2C10%2C-10%2C10%2C0%2C+x%5E2-2x-8%29+\"\r
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