document.write( "Question 1170536: The standard form equation of the parabola with vertex at (1, 2), latus rectum is 8, opens downward. \n" ); document.write( "

Algebra.Com's Answer #795395 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Vertex form of the equation is

\n" ); document.write( " $\"y+=+%28%281%2F%284p%29%29%28x-h%29%5E2%29%2Bk\"$

\n" ); document.write( "where the vertex is (h,k) and p is the directed distance from the directrix to the vertex and from the vertex to the focus.

\n" ); document.write( "With the equation in this form, |4p| is also the length of the latus rectum.

\n" ); document.write( "With the parabola opening downward, p is negative, so 4p = -8.

\n" ); document.write( "Then you have all the parts you need to write the equation in vertex form:

\n" ); document.write( " $\"y+=+%28%28-1%2F8%29%28x-1%29%5E2%29%2B2\"$

\n" ); document.write( "Convert that to any desired form.

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

\n" );