document.write( "Question 1190538: Find the quadratic function y=a(x−h)2 whose graph passes through the given points.
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Algebra.Com's Answer #822220 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Find the quadratic function y=a(x−h)2 whose graph passes through the given points.
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document.write( "Let's consider the point (2,0) first.\r\n" );
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document.write( "The fact that it belongs to the given form parabola MEANS that\r\n" );
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document.write( "    0 = a*(2-h)^2\r\n" );
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document.write( "which, with a=/=0, IMPLIES  h= 2.\r\n" );
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document.write( "So, half of the problem is just solved, and we know that h= 2.\r\n" );
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document.write( "THEREFORE, we can re-write the quadratic function in the form\r\n" );
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document.write( "    y = a*(x-2)^2.\r\n" );
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document.write( "Now consider the second point, (4,-2).\r\n" );
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document.write( "The fact that it belongs to the given form parabola MEANS that\r\n" );
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document.write( "    -2 = a*(4-2)^2,   or   -2 = a*2^2,    or   -2 = 4a\r\n" );
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document.write( "which implies  a=  = -0.5.\r\n" );
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document.write( "So, the quadratic function is  y = -0.5*(x-2)^2,   and  h= 2, a= -0.5.    ANSWER\r\n" );
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