document.write( "Question 1206777: What is the range of y = -x^2 - 2x + 3
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Algebra.Com's Answer #844410 by ikleyn(52779) $\"\"$ $\"About$

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document.write( "Function y(x) is a parabola opened downward.\r\n" );
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document.write( "The vertex is at  x =  = = \" ' =  = -1.\r\n" );
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document.write( "The maximum value of  y(x)  is at  x = -1:   = -(-1)^2 - 2*(-1) + 3 = -1 + 2 + 3 = 4.\r\n" );
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document.write( "In case (A),  the value   = -1  is in the domain;  THEREFORE,\r\n" );
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document.write( "the  ANSWER  to (A) is :  at x <=4,  the range of  y(x)  is  (-oo,] = (-oo,4].\r\n" );
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document.write( "In case (B), the value of  = -1 is  out the domain of y(x);  THEREFORE,\r\n" );
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document.write( "    the  ANSWER  to (B) is :  at x <= -4,  the range of  y(x)  is  (-oo,y(-4)].\r\n" );
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document.write( "    y(-4) = -(-4)^2 - 2*(-4) + 3 = -16 + 8  + 3 = -5;  so,  the range of  y(x)  is  (-oo,-5].\r\n" );
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