document.write( "Question 911490: I have to find the coordinates of the focus, vertex, axis of symmetry, and directrix.\r
\n" ); document.write( "\n" ); document.write( "x=1/4y^2-1/2y-3\r
\n" ); document.write( "\n" ); document.write( "I got stuck after I factored out the 1/4. Thank you in advance! \n" ); document.write( "
Algebra.Com's Answer #553128 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
\"x\"\"%22%22=%22%22\"\"expr%281%2F4%29y%5E2-expr%281%2F2%29y-3\"
\n" ); document.write( "
\r\n" );
document.write( "The easiest way when there are fractions is to clear of fractions\r\n" );
document.write( "first.  Multiply through by 4\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\"4x\"\"%22%22=%22%22\"\"y%5E2-2y-12\"\r\n" );
document.write( "\r\n" );
document.write( "Add 12 to both sides\r\n" );
document.write( "\r\n" );
document.write( "\"4x%2B12\"\"%22%22=%22%22\"\"y%5E2-2y\"\r\n" );
document.write( "\r\n" );
document.write( "Complete the square on the right:\r\n" );
document.write( "\r\n" );
document.write( "Multiply the coefficient of y by \"1%2F2\": \"2%2A%281%2F2%29\" = -1\r\n" );
document.write( "Square that result \"%28-1%29%5E2=%22%22%2B1\"\r\n" );
document.write( "Add +1 to both sides\r\n" );
document.write( "\r\n" );
document.write( "\"4x%2B13\"\"%22%22=%22%22\"\"y%5E2-2y%2B1\"\r\n" );
document.write( "\r\n" );
document.write( "Factor the right side:\r\n" );
document.write( "\r\n" );
document.write( "       \"y%5E2-2y%2B1=%28y-1%29%28y-1%29=%28y-1%29%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"4x%2B13\"\"%22%22=%22%22\"\"%28y-1%29%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "Factor 4 out of the left sides:\r\n" );
document.write( "\r\n" );
document.write( "\"4%28x%2B13%2F4%29\"\"%22%22=%22%22\"\"%28y-1%29%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "Multiply both sides by \"1%2F4\"\r\n" );
document.write( "\r\n" );
document.write( "\"x%2B13%2F4\"\"%22%22=%22%22\"\"expr%281%2F4%29%28y-1%29%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "Compare to \r\n" );
document.write( "\r\n" );
document.write( "\"x-h\"\"%22%22=%22%22\"\"4p%28y-k%29%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "and we have vertex = (h,k) = (\"-13%2F4\",1), 4p=\"1%2F4\", p=\"1%2F16\"\r\n" );
document.write( "\r\n" );
document.write( "It is a parabola with horizontal axis of symmetry, the green line below\r\n" );
document.write( "whose equation is y=1, since 1 is the y-coordinate of the vertex.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To find the focus we know it is p=\"1%2F16\" of a unit right of the vertex,\r\n" );
document.write( "so we add \"1%2F16\" to the x-coordinate of the vertex:\r\n" );
document.write( "\r\n" );
document.write( "\"-13%2F4%2B1%2F16=-52%2F16%2B1%2F16=-51%2F16\" and the y-coordinate of the focus is\r\n" );
document.write( "the same as the y-coordinate of the vertex, or 1.\r\n" );
document.write( "\r\n" );
document.write( "So the focus is the point (\"-51%2F16\",1)\r\n" );
document.write( "\r\n" );
document.write( "The directrix is a blue line p=\"1%2F16\" of a unit left of the vertex.\r\n" );
document.write( "\"-13%2F4-1%2F16=-52%2F16-1%2F16=-53%2F16\"\r\n" );
document.write( "\r\n" );
document.write( "So the equation of the directrix is \"x=-53%2F16\"\r\n" );
document.write( "\r\n" );
document.write( "The focus is the point (\"-51%2F16\",1) marked just right of the vertex \r\n" );
document.write( "and the directrix is the blue line \"x=-53%2F16\":\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );