document.write( "Question 414929: Find an equation of the parabola which contains a minimum point at (2,-1) and ordered pair (-1,7) \n" ); document.write( "
Algebra.Com's Answer #290972 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Find an equation of the parabola which contains a minimum point
\n" ); document.write( "at (2,-1) and ordered pair (-1,7)
\n" ); document.write( "
\r\n" );
document.write( "Here are the points plotted:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The equation of a parabola with vertex (h,k) is\r\n" );
document.write( "\r\n" );
document.write( "y = a(x - h)² + k\r\n" );
document.write( "\r\n" );
document.write( "The vertex is the minimum point, so\r\n" );
document.write( "\r\n" );
document.write( "(h,k) = (2,-1)\r\n" );
document.write( "\r\n" );
document.write( "We substitute h and k\r\n" );
document.write( "\r\n" );
document.write( "y = a(x - 2)² + (-1)\r\n" );
document.write( "\r\n" );
document.write( "y = a(x - 2)² - 1\r\n" );
document.write( "\r\n" );
document.write( "So we have everything but 'a'.\r\n" );
document.write( "\r\n" );
document.write( "So we substitute the point (x,y) = (-1,7)\r\n" );
document.write( "\r\n" );
document.write( "7 = a(-1 - 2)² - 1\r\n" );
document.write( "\r\n" );
document.write( " 7 = a(-3)² - 1\r\n" );
document.write( "\r\n" );
document.write( " 7 = a(9) - 1\r\n" );
document.write( "\r\n" );
document.write( " 7 = 9a - 1\r\n" );
document.write( "\r\n" );
document.write( " 8 = 9a\r\n" );
document.write( "\r\n" );
document.write( "\"8%2F9\" = a\r\n" );
document.write( "\r\n" );
document.write( "So the equation of the parabola is\r\n" );
document.write( "\r\n" );
document.write( "y = \"8%2F9\"(x - 2)² - 1\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "Edwin
\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );