document.write( "Question 141028: What is the vertex and focus of the parabola whose equation is $\"%28y-8%29%5E2+=+-4%28x-4%29\"$ ? \n" ); document.write( "

Algebra.Com's Answer #102693 by Edwin McCravy(20059) $\"\"$ $\"About$

You can put this solution on YOUR website!
What is the vertex and focus of the parabola whose equation is\r
\n" ); document.write( "\n" ); document.write( " $\"%28y-8%29%5E2+=+-4%28x-4%29\"$ ?
\n" ); document.write( "

\r\n" );
document.write( "You must memorize:\r\n" );
document.write( "\r\n" );
document.write( "\"U-parabolas\"\r\n" );
document.write( "\r\n" );
document.write( "Parabolas which open upward or downward have equation:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "with vertex (,), focus (,),\r\n" );
document.write( "\r\n" );
document.write( "the horizontal line which is the directrix has the\r\n" );
document.write( "equation .\r\n" );
document.write( "\r\n" );
document.write( "the vertical line which is the axis of symmetry has the\r\n" );
document.write( "equation .\r\n" );
document.write( " \r\n" );
document.write( "If p is positive the parabola opens upward. If p is\r\n" );
document.write( "negative the parabola opens downward\r\n" );
document.write( "\r\n" );
document.write( "-----\r\n" );
document.write( "\r\n" );
document.write( "C-parabolas\r\n" );
document.write( "\r\n" );
document.write( "Parabolas which open rightward or leftward have equation:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "with vertex (,), focus (,),\r\n" );
document.write( "\r\n" );
document.write( "the vertical line which is the directrix has the\r\n" );
document.write( "equation .\r\n" );
document.write( "\r\n" );
document.write( "the horizontal line which is the axis of symmetry has the\r\n" );
document.write( "equation .\r\n" );
document.write( "\r\n" );
document.write( "If p is positive the parabola opens rightward. If p is\r\n" );
document.write( "negative the parabola opens leftward.\r\n" );
document.write( "\r\n" );
document.write( "----\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "we compare this to\r\n" );
document.write( "\r\n" );
document.write( ", so the parabola opens right or left\r\n" );
document.write( "\r\n" );
document.write( " so \r\n" );
document.write( "\r\n" );
document.write( " so \r\n" );
document.write( "\r\n" );
document.write( " so , a negative number, so the\r\n" );
document.write( "parabola opens left\r\n" );
document.write( "\r\n" );
document.write( "So the vertex is (,) = (4,8)\r\n" );
document.write( "\r\n" );
document.write( "The focus is (, ) = (,) = (,) = (,)\r\n" );
document.write( "\r\n" );
document.write( "the vertical line which is the directrix has the\r\n" );
document.write( "equation , or  or  or \r\n" );
document.write( "\r\n" );
document.write( "the vertical line which is the axis of symmetry has the\r\n" );
document.write( "equation , or .\r\n" );
document.write( "\r\n" );
document.write( "To draw the parabola,  plot the focus, vertex, and directrix\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Draw a line from the focus thru to vertex to the directrix.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Use that line as a side of a square, draw one square above:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "and draw another square below:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Finally sketch in the parabola with the vertex (,)\r\n" );
document.write( "passing through corners of those two squares.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );