document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=542528>Question 542528</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have to find the vertex, axis of symmetry, minimum or maximum value, and range of the parabola. the formula is y=ax^2+bx+c <BR>\n" );
document.write( "Question: y=2x^2-6x+3<BR>\n" );
document.write( "What i have so far:<BR>\n" );
document.write( "y=2x^2-6x+3<BR>\n" );
document.write( "-b/2a=-(-6)/2(2)=6/4=3/2<BR>\n" );
document.write( "y=2(3/2)^2-6(3/2)+3<BR>\n" );
document.write( "  2(9/4)-(-18)/2<BR>\n" );
document.write( "I am stuck, I'm not sure if im doing it right but if you could help explain it to me that would be awsome! thank you!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #354630 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=354630\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2x%5E2-6x%2B3 ALIGN=MIDDLE  ALT=\"y+=+2x%5E2-6x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You have correctly found the x-coordinate of the vertex:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3%2F2 ALIGN=MIDDLE  ALT=\"x+=+3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and you have made a start on finding the corresponding y-coordinate by substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3%2F2 ALIGN=MIDDLE  ALT=\"x+=+3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the given quadratic equation to solve for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2%283%2F2%29%5E2-6%283%2F2%29%2B3 ALIGN=MIDDLE  ALT=\"y+=+2%283%2F2%29%5E2-6%283%2F2%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2%289%2F4%29-6%283%2F2%29%2B3 ALIGN=MIDDLE  ALT=\"y+=+2%289%2F4%29-6%283%2F2%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+9%2F2-18%2F2%2B6%2F2 ALIGN=MIDDLE  ALT=\"y+=+9%2F2-18%2F2%2B6%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-3%2F2 ALIGN=MIDDLE  ALT=\"y+=+-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The coordinates of the vertex are: (3/2, -3/2)<BR>\n" );
document.write( "The vertex is a minimum (the parabola opens upward) which is indicated by the positive coefficient of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > term.<BR>\n" );
document.write( "The axis of symmetry is give by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+3%2F2 ALIGN=MIDDLE  ALT=\"x+=+3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is the equation of the vertical line passing through the point (3/2, -3/2). (the vertex.)<BR>\n" );
document.write( "The range consists of all of the valid y-values.<BR>\n" );
document.write( "Since the y=coordinate of the vertex (a minimum) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-3%2F2 ALIGN=MIDDLE  ALT=\"y+=+-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > it is clear that the range is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and above.<BR>\n" );
document.write( "So the range can be written as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%3E=-3%2F2 ALIGN=MIDDLE  ALT=\"y%3E=-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can see this from the graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C5%2C-3%2C10%2C2x%5E2-6x%2B3%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C5%2C-3%2C10%2C2x%5E2-6x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );