document.write( "Question 1209281: The parabola y = ax^2 + bx + c is graphed below. Find a \cdot b \cdot c. (The grid lines are one unit apart.)\r
\n" ); document.write( "\n" ); document.write( "The parabola passes through (-5,-13), (2,7), and (4,-5). \n" ); document.write( "
Algebra.Com's Answer #848127 by mccravyedwin(407)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Let's plot the points and sketch a parabola through them:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\"y+=+ax%5E2+%2B+bx+%2B+c\"\r\n" );
document.write( "\r\n" );
document.write( "Substitute each point:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Simplify and put the constants on the right.\r\n" );
document.write( "\r\n" );
document.write( "\"system%2825a+-+5b+%2B+c=-13%2C%0D%0A4a+%2B+2b+%2B+c=7%2C%0D%0A16a+%2B+4b+%2B+c=-5%29\"\r\n" );
document.write( "\r\n" );
document.write( "Subtract the 2nd and 3rd equation from the first\r\n" );
document.write( "to eliminate c\r\n" );
document.write( "\r\n" );
document.write( "\"system%2821a-7b=-20%2C9a-9b=-8%29\"\r\n" );
document.write( "\r\n" );
document.write( "Multiply the 1st by 9 and the 2nd by -7 to eliminate b\r\n" );
document.write( "\r\n" );
document.write( "\"system%28189a-63b=-180%2C-63a%2B63b=56%29\"\r\n" );
document.write( "\r\n" );
document.write( "Add the equations:\r\n" );
document.write( "\r\n" );
document.write( "\"126a=-124\"\r\n" );
document.write( "\r\n" );
document.write( "\"a=-124%2F126\"\r\n" );
document.write( "\r\n" );
document.write( "\"a=-62%2F63\"\r\n" );
document.write( "\r\n" );
document.write( "Go back to\r\n" );
document.write( "\r\n" );
document.write( "\"system%2821a-7b=-20%2C9a-9b=-8%29\"\r\n" );
document.write( "\r\n" );
document.write( "Multiply the 1st by 9 and the 2nd by -21 to eliminate a\r\n" );
document.write( "\r\n" );
document.write( "\"system%28189a-63b=-180%2C-189a%2B189b=168%29\"\r\n" );
document.write( "\r\n" );
document.write( "Add the equations:\r\n" );
document.write( "\r\n" );
document.write( "\"126b=-12\"\r\n" );
document.write( "\r\n" );
document.write( "\"b=%28-12%29%2F126\"\r\n" );
document.write( "\r\n" );
document.write( "\"b=-2%2F21\"\r\n" );
document.write( "\r\n" );
document.write( "Go back to the easiest one of the original\r\n" );
document.write( "equations:\r\n" );
document.write( "\r\n" );
document.write( "\"4a+%2B+2b+%2B+c=7\"\r\n" );
document.write( "\r\n" );
document.write( "\"4%28-62%2F63%29+%2B+2%28-2%2F21%29+%2B+c=7\"\r\n" );
document.write( "\r\n" );
document.write( "\"-248%2F63-4%2F21%2Bc=7\"\r\n" );
document.write( "\r\n" );
document.write( "Multiply through by 63:\r\n" );
document.write( "\r\n" );
document.write( "\"-248-12%2B63c=441\"\r\n" );
document.write( "\r\n" );
document.write( "\"-260%2B63c=441\"\r\n" );
document.write( "\r\n" );
document.write( "\"63c=701\"\r\n" );
document.write( "\r\n" );
document.write( "\"c=701%2F63\"\r\n" );
document.write( "\r\n" );
document.write( "So \"abc\"\"%22%22=%22%22\"\"%28-62%2F63%29%28-2%2F21%29%28701%2F63%29\"\"%22%22=%22%22\"\"86924%2F83349\"\r\n" );
document.write( "\r\n" );
document.write( "Yes, your teacher should be fired, for they do not know how to teach\r\n" );
document.write( "mathematics.  No competent teacher would assign such a problem as this!\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );