document.write( "Question 142052: Identify vertex, focus, directrix, axis of symmetry and latus rectum from the following parabola equation:
\n" ); document.write( " $\"x=%281%2F8%29%28y%2B1%29%5E2%2B3\"$ \n" ); document.write( "

Algebra.Com's Answer #103457 by Edwin McCravy(20056) $\"\"$ $\"About$

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Identify vertex, focus, directrix, axis of symmetry and latus rectum from the following parabola equation:
\n" ); document.write( " $\"x=%281%2F8%29%28y%2B1%29%5E2%2B3\"$ \r
\n" ); document.write( "\n" ); document.write( "Two things you must know about parabolas, their graphs
\n" ); document.write( "and their equations \r
\n" ); document.write( "\n" ); document.write( "1. The parabola whose equation is\r
\n" ); document.write( "\n" ); document.write( " $\"y-k=4p%28x-h%29%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( "opens upward if p is positive, and downward if p is negative.
\n" ); document.write( "It has:\r
\n" ); document.write( "\n" ); document.write( "vertex, the point (h,k),
\n" ); document.write( "focus, the point (h,k+p),
\n" ); document.write( "directrix, the horizontal line whose equation is y=k-p
\n" ); document.write( "length of latus rectum = 4p,
\n" ); document.write( "endpoints of the latus rectum, the points (h-2p,k+p),(h+2p,k+p)\r
\n" ); document.write( "\n" ); document.write( "2. The parabola whose equation is\r
\n" ); document.write( "\n" ); document.write( " $\"x-h=4p%28y-k%29%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( "opens to the right if p is positive, and
\n" ); document.write( "to the left if p is negative.
\n" ); document.write( "It has:\r
\n" ); document.write( "\n" ); document.write( "vertex, the point (h,k),
\n" ); document.write( "focus, the point (h+p,k),
\n" ); document.write( "directrix, the vertical line whose equation is x=h-p
\n" ); document.write( "length of latus rectum = 4p,
\n" ); document.write( "endpoints of the latus rectum, the points (h+p,k-2p),(h+p,k+2p)\r
\n" ); document.write( "\n" ); document.write( "Your parabola is the second type:\r
\n" ); document.write( "\n" ); document.write( " $\"x=%281%2F8%29%28y%2B1%29%5E2%2B3\"$ \r
\n" ); document.write( "\n" ); document.write( "or\r
\n" ); document.write( "\n" ); document.write( " $\"x-3=%281%2F8%29%28y%2B1%29%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( "Compare that to\r
\n" ); document.write( "\n" ); document.write( " $\"x-h=4p%28y-k%29%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-h=-3\"$ so $\"h=3\"$
\n" ); document.write( " $\"4p=1%2F8\"$ so $\"p=1%2F32\"$
\n" ); document.write( " $\"-k=1\"$ so $\"k=-1\"$ \r
\n" ); document.write( "\n" ); document.write( "It opens to the right because $\"p=1%2F32\"$ , a positive number.\r
\n" ); document.write( "\n" ); document.write( "It has:\r
\n" ); document.write( "\n" ); document.write( "vertex, the point (h,k) = ( $\"3\"$ , $\"-1\"$ )
\n" ); document.write( "focus, the point (h+p,k) = ( $\"3%2B1%2F32\"$ , $\"-1\"$ ) = ( $\"97%2F32\"$ , $\"-1\"$ )
\n" ); document.write( "directrix, the vertical line whose equation is $\"x=h-p\"$ or $\"x=3-1%2F32\"$ or $\"x+=95%2F32\"$
\n" ); document.write( "length of latus rectum = $\"4p\"$ = $\"4%281%2F32%29\"$ = $\"4%2F32\"$ = $\"1%2F8\"$
\n" ); document.write( "endpoints of the latus rectum, the points ( $\"h%2Bp\"$ , $\"k-2p\"$ ) and ( $\"h%2Bp\"$ , $\"k%2B2p\"$ ), or ( $\"97%2F32\"$ , $\"-17%2F16\"$ ) and $\"97%2F32\"$ , $\"-15%2F16\"$ )\r
\n" ); document.write( "\n" ); document.write( "The parabola looks like this. The vertical line is the directrix.
\n" ); document.write( "The focus is the little dot just inside the parabola. I won't try to
\n" ); document.write( "draw the latus rectum. It is a very short line, only $\"1%2F8\"$ of a
\n" ); document.write( "unit that goes across the parabola through the focus. \r
\n" ); document.write( "\n" ); document.write( "

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

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