document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=368649>Question 368649</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me find the vertex and factor the equation of y=-16x^2+24x\r<BR>\n" );
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document.write( "so far for factoring it I have y=-8x(2x-3) but I am not sure if I did that right. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #262948 by </B><A HREF=/tutors/aboutme.mpl?userid=lefty4ever26><B>lefty4ever26(59)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lefty4ever26><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=lefty4ever26><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=262948\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have it factored right...Set equal to 0 to find x values (there will be 2)\r<BR>\n" );
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document.write( "0=-8x(2x-3)<BR>\n" );
document.write( "-8x=0  2x-3=0<BR>\n" );
document.write( "x=0 and x=3/2  These are the y intercepts and we know from the function that it is an upside down parabola. (because of the -16x^2)  \r<BR>\n" );
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document.write( "To find the maximum point (which would be the vertex) take the derivative of the function<BR>\n" );
document.write( "y=-16x^2+24x<BR>\n" );
document.write( "y'=-32x+24    Set equal to 0 and solve for x<BR>\n" );
document.write( "-32x+24=0<BR>\n" );
document.write( "x=3/4  Plug x=3/4 back into the original function\r<BR>\n" );
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document.write( "y=-16(3/4)^2+24(3/4)  Solve for y\r<BR>\n" );
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document.write( "y=-9+18=9.  So your vertex is at the point (3/4,9)\r<BR>\n" );
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