document.write( "Question 683603: what is the vertex form of y=-1/2x^2+4x-14 \n" ); document.write( "
Algebra.Com's Answer #423633 by Edwin McCravy(20055) $\"\"$ $\"About$
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document.write( "y = x² + 4x - 14\r\n" );
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document.write( "Clear of fractions:\r\n" );
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document.write( "2y = -x² + 8x - 28\r\n" );
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document.write( "Factor -1 out of first two terms on the right:\r\n" );
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document.write( "2y = -1(x² - 8x) - 28\r\n" );
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document.write( "Change the parentheses to brackets so it can contain parentheses:\r\n" );
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document.write( "2y = -1[x² - 8x] - 28\r\n" );
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document.write( "To complete the square inside the bracket:\r\n" );
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document.write( "1.  Take one-half of the coefficient of x.   ·(-8) = -4\r\n" );
document.write( "2.  Square the result.                       (-4)² = 16\r\n" );
document.write( "3.  Add it then subtract it in the bracket:   Add + 16 - 16\r\n" );
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document.write( "2y = -1[x² - 8x + 16 - 16] - 28\r\n" );
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document.write( "Factor the first three terms inside the bracket as a perfect square:\r\n" );
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document.write( "2y = -1[(x-4)² - 16] - 28\r\n" );
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document.write( "Remove the bracket by distributing the -1 leaving the parentheses intact:\r\n" );
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document.write( "2y = -1(x-4)² + 16 - 28\r\n" );
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document.write( "Combine the terms +16 - 28 as -12\r\n" );
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document.write( "2y = -1(x-4)² - 12\r\n" );
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document.write( "Solve for y by dividing through by 2\r\n" );
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document.write( " y = (x-4)² - 6\r\n" );
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document.write( "Compare that to the standard vertex form:\r\n" );
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document.write( " y = a(x-h)² + k\r\n" );
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document.write( "We see that the vertex (h,k) is (4,-6) and from the original\r\n" );
document.write( "equation y = x² + 4x - 14 tells us that the y-intercept\r\n" );
document.write( "is (0,-14) \r\n" );
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document.write( "The axis of symmetry is the vertical line through the vertex, and\r\n" );
document.write( "is therefore the vertical line whose equation is x=-4:\r\n" );
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document.write( "The point that matches the y-intercept on the other side of the\r\n" );
document.write( "axis of symmetry is (8,-14), so we plot that point:\r\n" );
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document.write( "and we sketch in the parabola:\r\n" );
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document.write( "Edwin
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