document.write( "Question 421654: How do I find the vertex, focus, directrix, axis of symmetry,
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Algebra.Com's Answer #294414 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
How do I find the vertex, focus, directrix, axis of symmetry,
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document.write( "    y - 1 = ¼(x + 2)²\r\n" );
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document.write( "Multiply both sides by 4\r\n" );
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document.write( "4*(y - 1) = 4*¼(x + 2)²\r\n" );
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document.write( "4*(y - 1) = 1(x + 2)²\r\n" );
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document.write( " 4(y - 1) = (x + 2)²\r\n" );
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document.write( "Swap left and right sides:\r\n" );
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document.write( "(x + 2)² = 4(y - 1)\r\n" );
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document.write( "Compare to this standard form:\r\n" );
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document.write( "(x - h)² = 4p(y - k)\r\n" );
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document.write( "which has these properties: \r\n" );
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document.write( "1. vertex is the point (h,k)\r\n" );
document.write( "2. line of symmetry equation is x = h\r\n" );
document.write( "3. focus is the point (h,k+p)\r\n" );
document.write( "4. directrix is the line whose equation is y = k-p \r\n" );
document.write( "5. length of latus rectum = |4p|\r\n" );
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document.write( "h = -2, k = 1, 4p = 4, so p = 1\r\n" );
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document.write( "So for this parabola,\r\n" );
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document.write( "1. vertex is the point (h,k) = (-2,1)\r\n" );
document.write( "2. line of symmetry equation is x = h or x = -2\r\n" );
document.write( "3. focus is the point (h,k+p) = (-2,1+1) = (-2,2)\r\n" );
document.write( "4. directrix is the line whose equation is y = k-p \r\n" );
document.write( "   or y = 1-1 or y = 0, which is the x-axis.  \r\n" );
document.write( "5. length of latus rectum = |4p| = 4\r\n" );
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document.write( "We plot the vertex (-2,1), focus (-2,2), the line of \r\n" );
document.write( "symmetry (in green), and the directrix y = 0 happens \r\n" );
document.write( "to be the the x-axis: \r\n" );
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document.write( "We draw the latus rectum which is a horizontal line \r\n" );
document.write( "segment 4p or 4 units long going through and centered \r\n" );
document.write( "on the focus:\r\n" );
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document.write( "Finally we draw the parabola through the ends of the \r\n" );
document.write( "latus rectum and through the vertex:\r\n" );
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document.write( "Edwin
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