document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=19280>Question 19280</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Without drawing the graph of the given equation, determine (a) how many x-intercepts the parabola has and (b) whether its vertex lies above or below the x- axis. <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #9304 by </B><A HREF=/tutors/aboutme.mpl?userid=mmm4444bot><B>mmm4444bot(95)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mmm4444bot><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=9304\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hello There:\r<BR>\n" );
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document.write( "The x-intercepts of a quadratic equation are the solutions when y = 0.\r<BR>\n" );
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document.write( "-x^2 + 2*x - 1 = 0\r<BR>\n" );
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document.write( "The value of the discriminant that appears in the quadratic formula tells us how many solutions there are.\r<BR>\n" );
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document.write( "In case you've not memorized the quadratic formula, the discriminant is:\r<BR>\n" );
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document.write( "sqrt[b^2 - 4*(a)*(c)]\r<BR>\n" );
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document.write( "If the value of this expression is negative, then there are no solutions (thus, there are no x-intercepts).\r<BR>\n" );
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document.write( "If the value of this expression is zero, then there is one solution (thus, one x-intercept).\r<BR>\n" );
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document.write( "If the value of this expression is positive, then there are two solutions (thus, two x-intercepts).\r<BR>\n" );
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document.write( "In your equation we have a = -1, b = 2, and c = -1.  Therefore, the value of the discriminant is:\r<BR>\n" );
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document.write( "sqrt[(2)^2 - 4*(-1)*(-1)]\r<BR>\n" );
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document.write( "sqrt(4 - 4)\r<BR>\n" );
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document.write( "sqrt(0)\r<BR>\n" );
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document.write( "The value of the discriminant is zero, so there is one x-intercept.  Since there is only one x-intercept, it must be the vertex of the parabola that is touching the x-axis.  Therefore, the vertex does not lie above or below the x-axis.\r<BR>\n" );
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document.write( "~ Mark<BR>\n" );
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