document.write( "Question 888045: 1. Solve the quadratic inequality. 2x^2+x-3>0\r
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\n" ); document.write( "\n" ); document.write( "2. Graph the quadratic inequality. Label vertex, axis, and intercepts.\r
\n" ); document.write( "\n" ); document.write( " y>4x^2-8x+3\r
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\n" ); document.write( "\n" ); document.write( "Do you plug it in just as a normal quadratic problem/formula, or I dont helP
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Algebra.Com's Answer #537021 by Fombitz(32388)\"\" \"About 
You can put this solution on YOUR website!
1.\r
\n" ); document.write( "\n" ); document.write( "You need to find the critical points of the function.
\n" ); document.write( "Break up the number line according to those critical points and test the inequality in those new regions.
\n" ); document.write( "\"2x%5E2%2Bx-3%3E0+\"
\n" ); document.write( "\"%28x-1%29%282x%2B3%29%3E0\"
\n" ); document.write( "In this case the critical points are,
\n" ); document.write( "\"x=1\" and \"x=-3%2F2\"
\n" ); document.write( "So break up the number line,
\n" ); document.write( "1.(\"-infinity\",\"-3%2F2\")
\n" ); document.write( "2.(\"-3%2F2\",\"1\")
\n" ); document.write( "3.(\"1\",\"infinity\")
\n" ); document.write( "Choose a point in each region and test the inequality.
\n" ); document.write( "Region 1: \"x=-2\"
\n" ); document.write( "\"2%28-2%29%5E2%2B%28-2%29-3%3E0\"
\n" ); document.write( "\"8-2-3%3E0\"
\n" ); document.write( "\"3%3E0\"
\n" ); document.write( "True
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\n" ); document.write( "Region 2: \"x=0\"\r
\n" ); document.write( "\n" ); document.write( "\"2%280%29%5E2%2B%280%29-3%3E0\"
\n" ); document.write( "\"-3%3E0\"
\n" ); document.write( "False
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\n" ); document.write( "Region 3: \"x=2\",
\n" ); document.write( "\"2%282%29%5E2%2B2-3%3E0\"
\n" ); document.write( "\"8%2B2-3%3E0\"
\n" ); document.write( "\"7%3E0\"
\n" ); document.write( "True
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\n" ); document.write( "So the solution region is the union of Region 1 and 3.\r
\n" ); document.write( "\n" ); document.write( "(\"-infinity\",\"-3%2F2\")U(\"1\",\"infinity\")
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\n" ); document.write( "2. Convert to vertex form.
\n" ); document.write( "\"y=4x%5E2-8x%2B3\"
\n" ); document.write( "\"y=4%28x%5E2-2x%29%2B3\"
\n" ); document.write( "\"y=4%28x%5E2-2x%2B1%29%2B3-4%281%29\"
\n" ); document.write( "\"y=4%28x-1%29%5E2-1\"
\n" ); document.write( "Vertex (\"1\",\"-1\")
\n" ); document.write( "Axis : \"x=1\"
\n" ); document.write( "X-Intercepts:
\n" ); document.write( "\"4%28x-1%29%5E2-1=0\"
\n" ); document.write( "\"4%28x-1%29%5E2=1\"
\n" ); document.write( "\"%28x-1%29%5E2=1%2F4\"
\n" ); document.write( "\"x-1=0+%2B-+1%2F2\"
\n" ); document.write( "\"x=1+%2B-+1%2F2\"
\n" ); document.write( "\"x=1%2F2\" and \"x=3%2F2\"
\n" ); document.write( "Y-intercept:
\n" ); document.write( "\"y=4%280%29%5E2-8%280%29%2B3\"
\n" ); document.write( "\"y=3\"
\n" ); document.write( ".
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\n" ); document.write( "\"graph%28300%2C300%2C-2%2C4%2C-2%2C4%2C4x%5E2-8x%2B3%29\"
\n" ); document.write( "Choose a point not on the parabola.
\n" ); document.write( "(0,0) is convenient.
\n" ); document.write( "Test the inequality.
\n" ); document.write( "\"y%3E4x%5E2-8x%2B3+\"
\n" ); document.write( "\"0%3E4%280%29-8%280%29%2B3\"
\n" ); document.write( "\"0%3E3\"
\n" ); document.write( "False, so shade the region that doesn't contain (0,0).\r
\n" ); document.write( "\n" ); document.write( "\"graph%28300%2C300%2C-2%2C4%2C-2%2C4%2Cy%3E4x%5E2-8x%2B3%29\" \n" ); document.write( "
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