Algebra.Com's Answer #351071 by Edwin McCravy(20059)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
What is the equation of a parabola that passes through the point at (3,-1), has its vertex at (2,-3) and opens to the left?
\n" );
document.write( "\r\n" );
document.write( "First we plot those two points to see if it's possible:\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "No it's not possible, for if it opens to the left, and have its\r\n" );
document.write( "vertex at (2,-3) it would have to look something like this:\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "But as you see it can't possibly go through (3,-1), for that's \r\n" );
document.write( "further to the right than the vertex, and the vertex has to be\r\n" );
document.write( "the rightmost point if it opens to the left.-\r\n" );
document.write( "\r\n" );
document.write( "Did you make a mistake and copy a sign wrong?\r\n" );
document.write( "\r\n" );
document.write( "Or maybe the parabola was supposed to open to the right like this.\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "So it would be possible for the parabola to open to the right\r\n" );
document.write( "but not the left:\r\n" );
document.write( "\r\n" );
document.write( "So I'll show you how to get the equation of this one:\r\n" );
document.write( "\r\n" );
document.write( "Use the form\r\n" );
document.write( "\r\n" );
document.write( "(y - k)² = 4p(x - h)\r\n" );
document.write( "\r\n" );
document.write( "where the vertex is (h,k). So we substitute (h,k) = (2,-3)\r\n" );
document.write( "\r\n" );
document.write( "(y - (-3))² = 4p(x - 2)\r\n" );
document.write( "\r\n" );
document.write( "(y + 3)² = 4p(x - 2)\r\n" );
document.write( "\r\n" );
document.write( "Now we substitute (x,y) = (2,-3)\r\n" );
document.write( "\r\n" );
document.write( "(-1 + 3)² = 4p(3 - 2)\r\n" );
document.write( "\r\n" );
document.write( " 2² = 4p(1)\r\n" );
document.write( "\r\n" );
document.write( " 4 = 4p\r\n" );
document.write( "\r\n" );
document.write( " 1 = p\r\n" );
document.write( "\r\n" );
document.write( "And substitute that in\r\n" );
document.write( "\r\n" );
document.write( "(y + 3)² = 4p(x - 2)\r\n" );
document.write( " \r\n" );
document.write( "(y + 3)² = 4(1)(x - 2)\r\n" );
document.write( "\r\n" );
document.write( "(y + 3)² = 4(x - 2)\r\n" );
document.write( "\r\n" );
document.write( "That's the equation of the parabola with vertex\r\n" );
document.write( "at (2,-3) that goes through (3,-1) but that opens to\r\n" );
document.write( "the right. \r\n" );
document.write( "\r\n" );
document.write( "Edwin \n" );
document.write( " |