document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=846713>Question 846713</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write the equation of a parabola in the form y=ax2 + bx + c where a,b, and c are integers with no common factors, a>0, and the zeros of the parabola are -5/3 and 7/2.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #509890 by </B><A HREF=/tutors/aboutme.mpl?userid=josh_jordan><B>josh_jordan(263)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josh_jordan><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=josh_jordan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=509890\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the equation of the parabola in the standard form of ax^2 + bx + c, given the two zeroes, we need to place the zeroes in factor form.  When zeroes are fractions, take the denominator of each fraction and place it in front of the x in each factor, and use the numerator as our constant, and use the opposite sign of our zeroes.  For example, if one of our zeroes is 1/5, we would put this in factor form as (5x - 1), because we put the denominator (5) in front of x and use the numerator (1) as our constant, and the sign we would use is the opposite of the sign of the zero.  The zero is a positive fraction, so we will use a MINUS sign.  So, using these steps, we can put each of our given zeroes in factor form:\r<BR>\n" );
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document.write( "-5/3 = (3x + 5)\r<BR>\n" );
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document.write( "7/2 = (2x - 7)\r<BR>\n" );
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document.write( "Now that we have our two factors, all we need to do is multiply them using the FOIL method:\r<BR>\n" );
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document.write( "(3x + 5)(2x - 7) ----->\r<BR>\n" );
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document.write( "6x^2 - 21x + 10x - 35 ----->\r<BR>\n" );
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document.write( "6x^2 - 11x - 35\r<BR>\n" );
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document.write( "Therefore, the equation of a parabola in standard form y = ax^2 + bx + c, with the zeroes -5/3 and 7/2 (and with integers with no common factors, and with a > 0) is:\r<BR>\n" );
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document.write( "y = 6x^2 - 11x - 35 </SPAN>\n" );
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