document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=329600>Question 329600</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If h (x) = a x 2 + bx + c, where b 2 - 4ac < 0 and a < 0, which of the following statements must be true?<BR>\n" );
document.write( "I. The graph of h (x) has no points in the first<BR>\n" );
document.write( "or second quadrants.<BR>\n" );
document.write( "II. The graph of h (x) has no points in the third<BR>\n" );
document.write( "or fourth quadrants.<BR>\n" );
document.write( "III. The graph of h (x) has points in all quadrants.<BR>\n" );
document.write( "(A) I only<BR>\n" );
document.write( "(B) II only<BR>\n" );
document.write( "(C) III only<BR>\n" );
document.write( "(D) I and II only<BR>\n" );
document.write( "(E) None of the statements are true. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #236290 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=236290\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if b^2 - 4ac is smaller than 0, then the roots are not real which means that the equation does not cross the x-axis.\r<BR>\n" );
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document.write( "If a is less than 0, this means that the graph of the equation points up and opens down.\r<BR>\n" );
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document.write( "Take these two together and the graph of the equation must be below the x-axis.\r<BR>\n" );
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document.write( "Statement 1 looks true.\r<BR>\n" );
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document.write( "Statement 2 looks false.\r<BR>\n" );
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document.write( "Statement 3 looks false.\r<BR>\n" );
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document.write( "I would say the answer is statement 1 only, which would be selection A.\r<BR>\n" );
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document.write( "A graph that meets the criteria expressed above would be:\r<BR>\n" );
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document.write( "-x^2 + x - 1\r<BR>\n" );
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document.write( "In this equation:\r<BR>\n" );
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document.write( "a = -1<BR>\n" );
document.write( "b = 1<BR>\n" );
document.write( "c = -1\r<BR>\n" );
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document.write( "b^2 - 4ac would be equal to 1 - (4*-1*-1) = 1 - (4) = -3 which is < 0.<BR>\n" );
document.write( "a = -1 which is < 0.\r<BR>\n" );
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document.write( "The graph of this equation looks like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-x%5E2+%2B+x+-+1%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-x%5E2+%2B+x+-+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You can see that the graph of this equation is in Quadrants III and IV only.\r<BR>\n" );
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