document.write( "Question 371261: how do you complete the square, y=8-3x^2-2x
\n" ); document.write( "(3x^2)is suppose to be 3x squared \n" ); document.write( "
Algebra.Com's Answer #264495 by Edwin McCravy(20055) $\"\"$ $\"About$
You can put this solution on YOUR website!
\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Arrange the right side in descending order:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Factor -3 out of the first two terms on the right:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "[Note that I got the \r\n" );
document.write( " by dividing -2 by -3]\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To the side multiply the coefficient of x, which is  by ,\r\n" );
document.write( "which gives  then square it, getting , then add and\r\n" );
document.write( "subtract  after the \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Notice that the first three terms inside the parentheses, \r\n" );
document.write( " can be factored as  and\r\n" );
document.write( "then as .  So replace the first three terms by this:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Remove the larger outside parentheses leaving the smaller parentheses\r\n" );
document.write( "intact:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Reduce  to \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To add the last two terms:  , so\r\n" );
document.write( "the final answer is:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Compare that to\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "and , , \r\n" );
document.write( "\r\n" );
document.write( "so the vertex is the point \r\n" );
document.write( "\r\n" );
document.write( "the line of symmetry has the equation  or .\r\n" );
document.write( "\r\n" );
document.write( "We know it opens downward since \"a\" is a negative number.\r\n" );
document.write( "\r\n" );
document.write( "We find the y-intercept by substituting x = 0 in the original\r\n" );
document.write( "\r\n" );
document.write( "equation:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So the y-intecept is (0,8), \r\n" );
document.write( "\r\n" );
document.write( "We find the x-intercepts from the original equation,\r\n" );
document.write( "setting y=0\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Rewrite as\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Multiply through by -1\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " gives \r\n" );
document.write( "\r\n" );
document.write( " gives \r\n" );
document.write( "\r\n" );
document.write( "So the x-intercepts are the points (,0) and (-2,0)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "so we plot the vertex, the y-intercept, the x-intercepts,\r\n" );
document.write( "and the vertical line of symmetry:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "and sketch in the parabola graph, through those points,\r\n" );
document.write( "symmetrical about the green line of symmetry:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );