document.write( "Question 1202596: g(x) = x²+mx+b
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\n" ); document.write( "\n" ); document.write( "Two quadratic functions g and h are defined by the equations above. If h(x) is symmetrical about the y axis, what must be the value of m? \n" ); document.write( "

Algebra.Com's Answer #837525 by ikleyn(52802) $\"\"$ $\"About$

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\n" ); document.write( "g(x) = x²+mx+b
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\n" ); document.write( "Two quadratic functions g and h are defined by the equations above. If h(x) is symmetrical about the y axis, what must be the value of m?
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document.write( "h(x) = g(x-2) = (x-2)^2 + m*(x-2) + b = x^2 - 4x + 4 + mx - 2m + b = x^2 + (m-4)x + constant terms.\r\n" );
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document.write( "Since h(x) is symmetrical about the y-axis, it implies that m-4 = 0,\r\n" );
document.write( "i.e. m= 4.    ANSWER\r\n" );
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document.write( "Another explanation, expressed in other words, is that the plot of h(x) \r\n" );
document.write( "is the plot of g(x) shifted 2 units right.\r\n" );
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document.write( "Since h(x) is symmetric about y-axis, it means that the symmetry line of g(x) \r\n" );
document.write( "is x= -2.\r\n" );
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document.write( "In turn, it means that m= 4 in the expression of g(x), giving the same answer/value for m.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, with explanations.\r
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