document.write( "Question 655401: What are the x-intercepts of the parabola whose equation
\n" ); document.write( "is y = x² + 3x - 1 \n" ); document.write( "
Algebra.Com's Answer #409110 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "We can get points on the parabola, say these 6, \r\n" );
document.write( "by substituting x=-4, x=-3, x=-2, x=-1, x=0, x=1\r\n" );
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document.write( "(-4,3), (-3,-1), (-2,-3), (-1,-3), (0,-1), (1,3),  \r\n" );
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document.write( "We sketch in the parabola:\r\n" );
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document.write( "We want to know where this parabola crosses the x-axis, which I\r\n" );
document.write( "have marked below with red circles:\r\n" );
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document.write( "From the graph it looks like the x-intercept on the left crosses somewhere\r\n" );
document.write( "between -3 and -4, and the x-intercept on the right crosses somewhere\r\n" );
document.write( "between 0 and 1.\r\n" );
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document.write( "To get these accurately we use the quadratic formula to find the values\r\n" );
document.write( "of x that cause y to be 0:\r\n" );
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document.write( "The solution to\r\n" );
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document.write( "ax² + bx + c = 0\r\n" );
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document.write( "is found by:\r\n" );
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document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"\r\n" );
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document.write( "Your problem is \r\n" );
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document.write( "x² + 3x - 1 = 0\r\n" );
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document.write( "So a=1, b=3, c=-1\r\n" );
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document.write( "\"x+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%29+\"\r\n" );
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document.write( "\"x+=+%28-3+%2B-+sqrt%289%2B4%29%29%2F2+\"\r\n" );
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document.write( "\"x+=+%28-3+%2B-+sqrt%2813%29%29%2F2+\"\r\n" );
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document.write( "Use a calculator with the +\r\n" );
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document.write( "\"x+=+%28-3+%2B+sqrt%2813%29%29%2F2+\" = 0.3027756377, which is the x-coordinate\r\n" );
document.write( "of the point circled on the right, and it is between 0 and 1.  So\r\n" );
document.write( "that x-intercept on the right is\r\n" );
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document.write( "(0.3027756377, 0)\r\n" );
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document.write( "Use a calculator with the -\r\n" );
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document.write( "\"x+=+%28-3+-+sqrt%2813%29%29%2F2+\" = -3.302775638, which is the x-coordinate\r\n" );
document.write( "of the point circled on the left, and it is between -3 and -4.  So\r\n" );
document.write( "that x-intercept on the left is\r\n" );
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document.write( "(-3.302775638, 0)\r\n" );
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document.write( "Or you can write them in radical (exact) form:\r\n" );
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document.write( "(\"%28-3+%2B+sqrt%2813%29%29%2F2+\", 0) and (\"%28-3+-+sqrt%2813%29%29%2F2+\", 0)\r\n" );
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document.write( " Edwin
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