document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206304>Question 1206304</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the equation in standard form y = ax^2 + bx + c if the roots ar 3 and - 6 and it passes through (2, -8)\r<BR>\n" );
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document.write( "A. y = x^2 - 3x - 18\r<BR>\n" );
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document.write( "B. y = x^2 + 3x + 18\r<BR>\n" );
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document.write( "C. y = x^2 + 3x - 18\r<BR>\n" );
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document.write( "D. y = x^2 - 3x - 18 </SPAN>\n" );
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document.write( "The quadratic term in all 4 answer choices is x^2, which means the equation in standard form has a=1.  Because of that, the given information that the graph passes through (2,-8) is not needed.<br><BR>\n" );
document.write( "Solution method 1...<br><BR>\n" );
document.write( "If the roots are 3 and -6, then the linear factors are (x-3) and (x-(-6))=(x+6).  The equation is then y = (x-3)(x+6) = x^2+3x-18.<br><BR>\n" );
document.write( "ANSWER: C<br><BR>\n" );
document.write( "Solution method 2...<br><BR>\n" );
document.write( "With a=1 in the standard form, Vieta's Theorem says the sum of the roots is -b and the product of the roots is c.<br><BR>\n" );
document.write( "The sum of the roots is 3+(-6) = -3, so b is 3; the product of the roots is 3(-6) = -18, so c is -18:  y = x^2+3x-18.<br><BR>\n" );
document.write( "ANSWER: C<br><BR>\n" );
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