document.write( "Question 1008646: given y=2x^2+bx+c, the minimum value is -3 and the graph intersects at (0,-1). Find the values of b and c. \n" ); document.write( "

Algebra.Com's Answer #624236 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

\r\n" );
document.write( "Instead of doing your problem for you, I'll do one exactly in every\r\n" );
document.write( "detail step-by-step like yours.  All you have to do is use it as a\r\n" );
document.write( "model and do the exact same steps.  So instead of your problem\r\n" );
document.write( "I will do this one with only the numbers changed. I didn't even\r\n" );
document.write( "change the 2 coefficient of x^2.\r\n" );
document.write( "\r\n" );
document.write( "given , the minimum value is -11 and the graph \r\n" );
document.write( "intersects at (0,-3). Find the values of b and c.\r\n" );
document.write( "\r\n" );
document.write( "Since the equation passes through (0,-3) we substitute\r\n" );
document.write( "(x,y) = (0,-3) into the given equation:\r\n" );
document.write( "\r\n" );
document.write( "-3=2(0)²+b(0)+c\r\n" );
document.write( "-3=0+0+c\r\n" );
document.write( "-3=c\r\n" );
document.write( "\r\n" );
document.write( "Therefore we already have the value of c, and\r\n" );
document.write( "\r\n" );
document.write( " becomes:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The minimum value of a quadratic equation is the y-coordinate\r\n" );
document.write( "of the vertex. The formula for the x-coordinate of the vertex is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Since a=2 this becomes \r\n" );
document.write( "\r\n" );
document.write( "Thus when we substitute the x coordinate of the vertex ,\r\n" );
document.write( "we will get the y coordinate of the vertex which will be the\r\n" );
document.write( "maximum value of -11.  So we substitute  for x and -11\r\n" );
document.write( "for y in\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Add 3 to both sides:\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( "\r\n" );
document.write( "Multiply through by 8\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( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus there are two solutions for b, and 1 solution for c\r\n" );
document.write( "\r\n" );
document.write( "Checking, we draw the graphs of\r\n" );
document.write( "\r\n" );
document.write( "  and  \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( "

\n" );