document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119197>Question 1119197</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Q57 For some constant &#945;, the graph of the quadratic function f(x) = – x^2+ 2&#945; x is a parabola with x-intercepts at A and B and vertex C. If the area of the triangle whose vertices are A, B, and <BR>\n" );
document.write( "C equals 125, what is the value of &#945;?<BR>\n" );
document.write( "A) -3 <BR>\n" );
document.write( "B) -5 <BR>\n" );
document.write( "C) 3<BR>\n" );
document.write( "D) 5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #734664 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=734664\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I will use k instead of &#945; for the constant we are looking for....<br><BR>\n" );
document.write( "The vertex of the parabola is when x = -b/(2a) = -2k/-2 = k; the value of the function at x=k is -k^2+2k^2 = k^2.<br><BR>\n" );
document.write( "So the vertex is C(k,k^2).<br><BR>\n" );
document.write( "The x-intercepts are A(0,0) and B(2k,0).<br><BR>\n" );
document.write( "Triangle ABC then has base 2k and altitude k; its area is (1/2) base times height = k^2.<br><BR>\n" );
document.write( "So k^2 = 125, making k=5*sqrt(5)... which is not one of the answer choices.<br><BR>\n" );
document.write( "The problem as you show it is flawed.<br><BR>\n" );
document.write( "Perhaps the area was supposed to be 25 instead of 125, making D the answer....?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );