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document.write( "The lady above mentioned the form of the parabola that is used when studying\r\n" );
document.write( "quadratic functions, y=a(x-h)²+k, when you are not concerned with the\r\n" );
document.write( "focus or the directrix. The form to use when you are studying\r\n" );
document.write( "conic sections is the other one she gave. When studying conic sections you \r\n" );
document.write( "use these two forms:\r\n" );
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document.write( "(x-h)² = 4p(y-k) and (y-k)² = 4p(x-h)\r\n" );
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document.write( "where |p| is the distance between the vertex and the focus,\r\n" );
document.write( "and (h,k) is the vertex.\r\n" );
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document.write( "The first one is for parabolas opening upward or downward.\r\n" );
document.write( "If p is positive the parabola opens upward, and if negative\r\n" );
document.write( "it opens downward.\r\n" );
document.write( "The second one is for parabolas opening rightward or leftward.\r\n" );
document.write( "If p is positive the parabola opens rightward, and if negative\r\n" );
document.write( "it opens leftward.\r\n" );
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document.write( "First we will plot the focus F(9,9) and draw the directrix,\r\n" );
document.write( "which is the line with the equation y=-5, which is a horizontal\r\n" );
document.write( "line 5 units below the x-axis, drawn in green below:\r\n" );
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document.write( "The vertex is a point half-way between the focus and the directrix.\r\n" );
document.write( "So we draw a line from the focus directly down to the directrix. I'll\r\n" );
document.write( "draw that one in blue. \r\n" );
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document.write( "The midpoint of that blue line is the vertex of the parabola. We know \r\n" );
document.write( "that its x-coordinate is the same as the x-coordinate of the focus, 9.\r\n" );
document.write( "We can find its y coordinate by averaging the y coordinate of the focus,\r\n" );
document.write( "9 and the y-coordinate of all points on the directrix, -5, averaging\r\n" );
document.write( "them is 
. So the vertex is V(9,2)\r\n" );
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document.write( "Now draw a square which has its left side as the blue line\r\n" );
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document.write( "Now draw a square which has its right side as the blue line\r\n" );
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document.write( "Now we can sketch in the parabola with its vertex and passing through the\r\n" );
document.write( "the corners of those two squares.\r\n" );
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document.write( "There are 7 units between the vertex and the focus, so p = 7, positive\r\n" );
document.write( "because the parabola opens upward. The vertex is (h,k).\r\n" );
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document.write( "So the equation of the parabola is of the form:\r\n" );
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document.write( " (x-h)² = 4p(y-k)\r\n" );
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document.write( "whete (h,k) = (9,2) and p = 7\r\n" );
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document.write( "Substituting\r\n" );
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document.write( " (x-9)² = 4(7)(y-2)\r\n" );
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document.write( " (x-9)² = 28(y-2)\r\n" );
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document.write( "BTW, you did not have to to be given the value of 4p which is 28.\r\n" );
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document.write( "Edwin
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