document.write( "Question 1037013: I need help making a graph from a table of values for this function
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\n" ); document.write( "\n" ); document.write( "Determine consecutive integer values of x between which each
\n" ); document.write( "real zero is located. \r
\n" ); document.write( "\n" ); document.write( "Between which two xconsecutive integers does the x-coordinate
\n" ); document.write( "of the relative maxima and relative minima occur? \n" ); document.write( "
Algebra.Com's Answer #651723 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "h(x) = x4 - 2x3 - 6x2 + 8x + 5 \r\n" );
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document.write( "y = h(-2) = (-2)4 - 2(-2)3 - 6(-2)2 + 8(2) + 5\r\n" );
document.write( "y = h(-2) = 16 - 2(8) - 6(4) + 16 + 5\r\n" );
document.write( "y = h(-2) = 16 - 16 - 24 + 21\r\n" );
document.write( "y = h(-2) = 0 - 24 + 21\r\n" );
document.write( "y = h(-2) = -3  \r\n" );
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document.write( "Do that also with x = -3,-1, 0, 1, 2, 3, 4\r\n" );
document.write( "and make this table:\r\n" );
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document.write( " x |y=h(x)     point\r\n" );
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document.write( "-3 | 62       (-3,62)   <-- too high to plot\r\n" );
document.write( "-2 | -3       (-2,-3)\r\n" );
document.write( "-1 | -6       (-1,-6)\r\n" );
document.write( " 0 |  5        (0,5) \r\n" );
document.write( " 1 |  6        (1,6)\r\n" );
document.write( " 2 | -3        (2,-3)\r\n" );
document.write( " 3 |  2        (3,2)   \r\n" );
document.write( " 4 | 69        (4,69)   <-- too high to plot.\r\n" );
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document.write( "Then plot them and draw a smooth curve through them:\r\n" );
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document.write( "There is a real zero between where x=-3 and where x=-2\r\n" );
document.write( "because when x is -3, y is 63, a positive number and\r\n" );
document.write( "when x=-2, y is -3, a negative number. So for the graph\r\n" );
document.write( "to get from a y-value that is positive a y-value that is \r\n" );
document.write( "negative, the graph must cross the x-axis between \r\n" );
document.write( "them. \r\n" );
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document.write( "There is a real zero between where x=-1 and where x=0\r\n" );
document.write( "because when x is -1, y is -6, a negative number and\r\n" );
document.write( "when x=0, y is 5, a negative number. So for the graph\r\n" );
document.write( "to get from a y-value that is negative to a a y-value \r\n" );
document.write( "that is positive, the graph must cross the x-axis between \r\n" );
document.write( "them. \r\n" );
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document.write( "There is a real zero between where x=1 and where x=2\r\n" );
document.write( "because when x is 1, y is 6, a positive number and\r\n" );
document.write( "when x=2, y is -3, a negative number. So for the graph\r\n" );
document.write( "to get from a y-value that is positive a y-value that is \r\n" );
document.write( "negative, the graph must cross the x-axis between \r\n" );
document.write( "them. \r\n" );
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document.write( "There is a real zero between where x=2 and where x=3\r\n" );
document.write( "because when x is 2, y is -3, a negative number and\r\n" );
document.write( "when x=3, y is 2, a positive number. So for the graph\r\n" );
document.write( "to get from a y-value that is negative a y-value that is \r\n" );
document.write( "positive, the graph must cross the x-axis between \r\n" );
document.write( "them. \r\n" );
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document.write( "Looks like the leftmost relative minimum point (\"valley\") occurs \r\n" );
document.write( "between where x = -2 and -1.\r\n" );
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document.write( "Looks like the only relative maximum point (\"peak\") occurs \r\n" );
document.write( "between where x = 0 and 1.\r\n" );
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document.write( "Looks like the rightmost relative minimum point (\"valley\") occurs \r\n" );
document.write( "between where x = 2 and 3.\r\n" );
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document.write( "Edwin
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