document.write( "Question 194756: Is this correct: What is the equation of a parabola with vertex (0,0) and focus (0,4)?
\n" ); document.write( "\"%28x-h%29%5E2+=+4p%28y-k%29\"
\n" ); document.write( "\"%28x-0%29%5E2+=+4%284%29%28y-0%29\"
\n" ); document.write( "\"%28x-0%29%5E2+=+16%28y-0%29\"\r
\n" ); document.write( "\n" ); document.write( "If not where did I go wrong? \n" ); document.write( "
Algebra.Com's Answer #146107 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Edwin's solution and graph:
\n" ); document.write( "
\r\n" );
document.write( "I think you're right, except maybe you'd want to erase\r\n" );
document.write( "the 0's in the final answer.\r\n" );
document.write( "\r\n" );
document.write( "I'll go through it.\r\n" );
document.write( "\r\n" );
document.write( "Draw the two points, vertex V(0,0) and the focus F(0,4)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We can tell the parabola opens upward since the focus\r\n" );
document.write( "is above the vertex.  The equation is \r\n" );
document.write( "\r\n" );
document.write( "\"%28x-h%29%5E2+=+4p%28y-k%29\"\r\n" );
document.write( "\r\n" );
document.write( "Where the vertex is (h,k), and p is the directed\r\n" );
document.write( "distance from the vertex to the focus.\r\n" );
document.write( "\r\n" );
document.write( "If we put our pencil on the vertex and go to the focus\r\n" );
document.write( "we move the pencil upward 4 units, so the parabolic constant\r\n" );
document.write( "p = +4.  (When the pencil moves downward in going from the\r\n" );
document.write( "vertex to the focus, then p is negative)\r\n" );
document.write( "\r\n" );
document.write( "The directed distance from the vertex to the focus in\r\n" );
document.write( "this problem is +4, and (h,k) = (0,0) so, substituting\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-h%29%5E2+=+4p%28y-k%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"%28x-0%29%5E2+=+4%284%29%28y-0%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"x%5E2+=+16y\"\r\n" );
document.write( "\r\n" );
document.write( "To draw the finished parabola, first draw the directrix\r\n" );
document.write( "which is a horizontal line p units on the other side of the \r\n" );
document.write( "vertex.  In this case it is 4 units below the vertex.  It\r\n" );
document.write( "has the eqution \"y=-4\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now draw a square with its left side as the line from the directrix\r\n" );
document.write( "to the focus:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now draw another square with its right side as the line from the directrix\r\n" );
document.write( "to the focus:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Finally sketch in the parabola passing through the \r\n" );
document.write( "upper far corners of the squares and through the vertex:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "
\n" );