Wtite the parabola in standard form :
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document.write( "a)\r\n" );
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document.write( " x² + 10x - 6y + 7 = 0\r\n" );
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document.write( "Since there is an x² term, isolate the terms in x on the left\r\n" );
document.write( "side of the equation:\r\n" );
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document.write( " x² + 10x = 6y - 7 \r\n" );
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document.write( "If x² had not had a coefficient of 1 then we woulfd\r\n" );
document.write( "have to divide through by it. But since x² has a 1\r\n" );
document.write( "coefficient this is not necessary]\r\n" );
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document.write( " x² + 10x = 6y - 7 \r\n" );
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document.write( "We complete the square:\r\n" );
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document.write( "1. Multiply the coefficient of x which is +10 by 
getting +5\r\n" );
document.write( "2. Square this, getting (+5)² = +25\r\n" );
document.write( "3. Add this to both sides of the equation:\r\n" );
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document.write( " x² + 10x + 25 = 6y - 7 + 25\r\n" );
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document.write( "The left side factors as (x+5)(x+5) or (x+5)²\r\n" );
document.write( "Combine like terms on the right side of the equation.\r\n" );
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document.write( "(x + 5)² = 6y + 18\r\n" );
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document.write( "Finally factor out the coefficient of y on the right\r\n" );
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document.write( "(x + 5)² = 6(y + 3)\r\n" );
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document.write( "That's the answer, but later you'll have to compare it to\r\n" );
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document.write( "(x - h)² = a(y - k)\r\n" );
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document.write( "And the vertex is (h,k) = (-5,-3) and since x is squared and not y,\r\n" );
document.write( "the parabola has a vertical axis of symmetry and since a = 6 and\r\n" );
document.write( "is positive the parabola opens upward.\r\n" );
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document.write( "(b) \r\n" );
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document.write( " y² + 8x - 2y = 15\r\n" );
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document.write( "Since there is a y² term, isolate the terms in y on the left\r\n" );
document.write( "side of the equation:\r\n" );
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document.write( " y² - 2y = -8x + 15 \r\n" );
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document.write( "If y² had not had a coefficient of 1 then we woulfd\r\n" );
document.write( "have to divide through by it. But since y² has a 1\r\n" );
document.write( "coefficient this is not necessary]\r\n" );
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document.write( " y² - 2y = -8x + 15 \r\n" );
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document.write( "We complete the square:\r\n" );
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document.write( "1. Multiply the coefficient of y which is -2 by getting -1\r\n" );
document.write( "2. Square this, getting (-1)² = +1\r\n" );
document.write( "3. Add this to both sides of the equation:\r\n" );
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document.write( " y² - 2y + 1 = -8x + 15 + 1\r\n" );
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document.write( "The left sides factors as (y-1)(y-1) or (y-1)²\r\n" );
document.write( "Combine like terms on the right side of the equation.\r\n" );
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document.write( "(y - 1)² = -8x + 16\r\n" );
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document.write( "Finally factor out the coefficient of x on the right\r\n" );
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document.write( "(y - 1)² = -8(x - 2)\r\n" );
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document.write( "That's the answer, but later you'll have to compare it to\r\n" );
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document.write( "(y - k)² = a(x - h)\r\n" );
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document.write( "And the vertex is (h,k) = (2,1) and since y is squared and not x,\r\n" );
document.write( "the parabola has a horizontal axis of symmetry and since a = -8 and\r\n" );
document.write( "is negative the parabola opens to the left.\r\n" );
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document.write( "Edwin
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