document.write( "Question 1100471: you use a system with three variables to find the equation of a parabola that passes through the points (-8,0) (2,-20) and (1,0). Your friend uses intercept form to find the equation. whose method is easier? justify your answer. \n" ); document.write( "

Algebra.Com's Answer #714962 by ikleyn(52778) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "In this case THE FASTEST METHOD is THIS:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "This parabola (quadratic polynomial) has the roots x= -8 and x= 1  (where y is equal to zero).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence, the quadratic polynomial has the form  p(x) = a*(x-(-8))*(x-1) = a(x+8)*(x-1) with the unknown coefficient \"a\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To determine the value of \"a\", use the condition/(the fact from the condition) that\r\n" );
document.write( "\r\n" );
document.write( "p(2) = -20 = a(2+8)*(2-1) = a*10*1 = 10*a.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It gives you   a =  = -2.\r\n" );
document.write( "\r\n" );
document.write( "and finally your polynomial has the form\r\n" );
document.write( "\r\n" );
document.write( "p(x) = -2*(x+8)*(x-1).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "You can transform it further to any form you wish.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Under this approach, you do not need solve any systems of equations.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If your friend uses this method, he is on the right track.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );