document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=602355>Question 602355</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,<BR>\n" );
document.write( "would you pls check if my answer is correct?<BR>\n" );
document.write( "1)Without drawing the graph of the equations, determine how many points the parabola has in common with the x-axis and whether its vertex lies above, on, or below the x-axis.<BR>\n" );
document.write( " a. y = 3x^2 – 12x + 12<BR>\n" );
document.write( " b. y = –2x^2 + x + 3<BR>\n" );
document.write( " <BR>\n" );
document.write( "My answer : a. 1 point in common; vertex on x-axis<BR>\n" );
document.write( " <BR>\n" );
document.write( "            b. 2 points in common; vertex above x-axis<BR>\n" );
document.write( " <BR>\n" );
document.write( "Thanks a lot,<BR>\n" );
document.write( " H.H<BR>\n" );
document.write( "P.S.:This is my 2nd submission for this question.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #380208 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=380208\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1)Without drawing the graph of the equations, determine how many points the parabola has in common with the x-axis and whether its vertex lies above, on, or below the x-axis.<BR>\n" );
document.write( " a. y = 3x^2 – 12x + 12<BR>\n" );
document.write( "Find the discriminant<BR>\n" );
document.write( "D = b^2 - 4ac<BR>\n" );
document.write( "D = (-12)^2 - 4*3*12<BR>\n" );
document.write( "D = 0 --> 1 real number solution<BR>\n" );
document.write( "It's actually 2 solutions that are equal, but that makes one point on the x-axis.<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( " b. y = –2x^2 + x + 3<BR>\n" );
document.write( "D = 1 - 4*-2*3<BR>\n" );
document.write( "D = 25<BR>\n" );
document.write( "D > 0 --> 2 real solutions, 2 crossings of the x-axis<BR>\n" );
document.write( "------------<BR>\n" );
document.write( " <BR>\n" );
document.write( "My answer : a. 1 point in common; vertex on x-axis<BR>\n" );
document.write( "Correct.<BR>\n" );
document.write( "============================================<BR>\n" );
document.write( "            b. 2 points in common; vertex above x-axis<BR>\n" );
document.write( "2 points.  The coefficient of the x^2 terms is negative, so it opens downward.<BR>\n" );
document.write( "--> vertex above the x-axis<BR>\n" );
document.write( "Correct. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );