document.write( "Question 1042755: Write the equation of the quadratic function with roots -9 and and -3 and a vertex at (-6, -1)
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Algebra.Com's Answer #657786 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Write the equation of the quadratic function with roots -9 and and -3 and a vertex at (-6, -1)
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document.write( "I know (and you should know it) that this function has a form \r\n" );
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document.write( "f(x) = a*(x-(-9)*(x-(-3)) = a*(x+9)*(x+3),\r\n" );
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document.write( "where \"a\" is a real constant.\r\n" );
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document.write( "To determine this constant, I will calculate the function f(x) at the point x = -6, where the vertex is. It is\r\n" );
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document.write( "f(-6) = a*(-6 +9)*(-6+3) = a*3*(-3) = -9a.\r\n" );
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document.write( "Thus, I must find the value of \"a\" from this equation: \r\n" );
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document.write( "f(-6) = -1,  which becomes  -9a = -1.\r\n" );
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document.write( "Hence,  a =  = .\r\n" );
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document.write( "Answer.  The function under the question is f(x) = .\r\n" );
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document.write( "You may open parentheses if you need.\r\n" );
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