document.write( "Question 1040224: I need help
\n" ); document.write( "When the range of x determined by
\n" ); document.write( "\"-ax%5E2%2Bbx%2B4%3E=0\" is \"-1%2F3%3C=x%3C=4\"\r
\n" ); document.write( "\n" ); document.write( "then a = ?, b = ?
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Algebra.Com's Answer #655031 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
When the range of x determined by
\n" ); document.write( "\"-ax%5E2%2Bbx%2B4%3E=0\" is \"-1%2F3%3C=x%3C=4\"\r
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In order for the function \r\n" );
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document.write( "\"y+=+-ax%5E2%2Bbx%2B4\"\r\n" );
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document.write( "to be greater than or equal to 0, its graph must be on or above the\r\n" );
document.write( "x-axis.  A quadratic equation is the equation of a parabola.  \r\n" );
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document.write( "So this is a parabola that opens downward\r\n" );
document.write( "and has x-intercepts (real zeros) at -1/3 and 4.\r\n" );
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document.write( "So we are to find the equation of the function\r\n" );
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document.write( "\"y+=+-ax%5E2%2Bbx%2B4\"\r\n" );
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document.write( "In order for it to have zeros -1/3 and 4,\r\n" );
document.write( "it must be of the form\r\n" );
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document.write( "\"y+=+-a%28x%2B1%2F3%29%28x-4%29\" \r\n" );
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document.write( "\"y+=+-a%28x%5E2-4x%2Bexpr%281%2F3%29x-4%2F3%29\"\r\n" );
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document.write( "\"y+=+-ax%5E2%2B4ax-expr%281%2F3%29ax%2Bexpr%284%2F3%29a\"\r\n" );
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document.write( "\"y+=+-ax%5E2%2B%284a-expr%281%2F3%29a%29x%2Bexpr%284%2F3%29a\"\r\n" );
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document.write( "We compare it to\r\n" );
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document.write( "\"y=-ax%5E2%2Bbx%2B4\"\r\n" );
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document.write( "The last (constant) terms must be the same, so\r\n" );
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document.write( "\"expr%284%2F3%29a=4\"\r\n" );
document.write( "\"4a=12\"\r\n" );
document.write( "\"a=3\"\r\n" );
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document.write( "Substituting in\r\n" );
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document.write( "\"y+=+-ax%5E2%2B%284a-expr%281%2F3%29a%29x%2Bexpr%284%2F3%29a\"\r\n" );
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document.write( "\"y+=+-3x%5E2%2B%284%2A3-expr%281%2F3%29%2A3%29x%2B3%2Aexpr%284%2F3%293\"\r\n" );
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document.write( "\"y+=+-3x%5E2%2B%2812-1%29x%2B4\"\r\n" );
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document.write( "\"y+=+-3x%5E2%2B11x%2B4\"\r\n" );
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document.write( "So a = 3 and b = 11\r\n" );
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document.write( "Edwin
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