document.write( "Question 112182: I am given three points on a graph (14,0), (10.5,1), (6.5,3) and am asked to find the equation for the parabola that passes through these points. I understand that the parabola must be positive and open upwards. Also, I know that the \"c\" value must be 14 because that is the y intercept. But, from then on, I really have no idea what to do. Could you please help me? \n" ); document.write( "

Algebra.Com's Answer #81884 by Edwin McCravy(20056) $\"\"$ $\"About$

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I am given three points on a graph (14,0), (10.5,1), (6.5,3) and am asked to find the equation for the parabola that passes through these points. I understand that the parabola must be positive and open upwards. Also, I know that the \"c\" value must be 14 because that is the y intercept. But, from then on, I really have no idea what to do. Could you please help me?\r
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document.write( "The c value is not what you thought.  \r\n" );
document.write( "You were thinking (14,0) was (0,14)\r\n" );
document.write( "but it's just backwards from that.\r\n" );
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document.write( "Here we go from scratch:\r\n" );
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document.write( "A quadratic function has a parabola for its graph and\r\n" );
document.write( "it must have an equation of thge form: \r\n" );
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document.write( "y = ax² + bx + c\r\n" );
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document.write( "So plug each of the points in that equation.\r\n" );
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document.write( "Plug in (x,y) = (14,0)\r\n" );
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document.write( "y = ax² + bx + c\r\n" );
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document.write( "0 = a(14)² + b(14) + c\r\n" );
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document.write( "0 = 196a + 14b + c\r\n" );
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document.write( "-------\r\n" );
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document.write( "Plug in (x,y) = (10.5,1)\r\n" );
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document.write( "y = ax² + bx + c\r\n" );
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document.write( "1 = a(10.5)² + b(10.5) + c\r\n" );
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document.write( "1 = 110.25a + 10.5b + c\r\n" );
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document.write( "-------\r\n" );
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document.write( "Plug in (x,y) = (6.5,3)\r\n" );
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document.write( "y = ax² + bx + c\r\n" );
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document.write( "3 = a(6.5)² + b(6.5) + c\r\n" );
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document.write( "3 = 42.25a + 6.5b + c\r\n" );
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document.write( "So we have this system\r\n" );
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document.write( "0 = 196a + 14b + c\r\n" );
document.write( "1 = 110.25a + 10.5b + c\r\n" );
document.write( "3 = 42.25a + 6.5b + c\r\n" );
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document.write( "or, putting the numbers on the right and lining up\r\n" );
document.write( "the letters:\r\n" );
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document.write( "   196a +   14b + c = 0\r\n" );
document.write( "110.25a + 10.5b + c = 1\r\n" );
document.write( " 42.25a +  6.5b + c = 3\r\n" );
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document.write( "Can you solve that system?  If not post again.  \r\n" );
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document.write( "The answers to that system are a = , b = , c = \r\n" );
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document.write( "So y = ax² + bx + c becomes\r\n" );
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document.write( "y = x² -x + \r\n" );
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document.write( "It has vertex (, )\r\n" );
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document.write( "Its x-intercepts are (14, 0) and (41/2, 0)\r\n" );
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document.write( "Its y intercept is (0, 41/5)\r\n" );
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document.write( "Its axis of symmetry has the equation x = \r\n" );
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document.write( "Its graph is this with the green line as the\r\n" );
document.write( "axis of symmetry:\r\n" );
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document.write( "Edwin

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