document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=214894>Question 214894</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help solving the quadratic function,For Each Funtion:(a) determine whether the graph opens down or up, (b) find the axis of symmetry, (c)find the vertex, (d)find the y-intercept,(e) find the zeros, and (f) graph the function<BR>\n" );
document.write( "the equation is: -x(x-3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #162342 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=162342\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%28x-3%29 ALIGN=MIDDLE  ALT=\"-x%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > rewrite as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-x%5E2%2B3x ALIGN=MIDDLE  ALT=\"y+=+-x%5E2%2B3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find:<BR>\n" );
document.write( "a) The graph opens downward as indicated by the negative value 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( "b) The axis of symmetry (AOS) is given by:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-b%2F2a ALIGN=MIDDLE  ALT=\"x+=+-b%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > where: a = -1 and b = 3.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-3%29%2F2%28-1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-3%29%2F2%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+=+3%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%28x+=+3%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is the equation of the AOS.<BR>\n" );
document.write( "c) The vertex is lies on the AOS and is found by using the equation of the AOS for the x-coordinate, then substituting this into the given quadratic equation to solve for the corresponding y-coordinate.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-x%5E2%2B3x ALIGN=MIDDLE  ALT=\"y+=+-x%5E2%2B3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute <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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-%283%2F2%29%5E2%2B3%283%2F2%29 ALIGN=MIDDLE  ALT=\"y+=+-%283%2F2%29%5E2%2B3%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Evaluate.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-%289%2F4%29%2B%289%2F2%29 ALIGN=MIDDLE  ALT=\"y+=+-%289%2F4%29%2B%289%2F2%29\"   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%2F4 ALIGN=MIDDLE  ALT=\"y+=+9%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The vertex is at: (3/2, 9/4)<BR>\n" );
document.write( "d) <BR>\n" );
document.write( "The y-intercept is found by setting x = 0 in the given quadratic equation and solving for y.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-x%5E2%2B3x ALIGN=MIDDLE  ALT=\"y+=+-x%5E2%2B3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitute x = 0.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+0 ALIGN=MIDDLE  ALT=\"y+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The y-intercept is at: (0, 0)<BR>\n" );
document.write( "e)<BR>\n" );
document.write( "The zeros are found by setting the given quadratic equation equal to zero and solving.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%5E2%2B3x+=+0 ALIGN=MIDDLE  ALT=\"-x%5E2%2B3x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor a -x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x%28x-3%29+=+0 ALIGN=MIDDLE  ALT=\"-x%28x-3%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply the zero product rule:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x+=+0 ALIGN=MIDDLE  ALT=\"-x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3+=+0 ALIGN=MIDDLE  ALT=\"x-3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > so that...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+=+0%29 ALIGN=MIDDLE  ALT=\"highlight%28x+=+0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x+=+3%29 ALIGN=MIDDLE  ALT=\"highlight%28x+=+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The zeros are at (0, 0) and (3, 0)<BR>\n" );
document.write( "f) <BR>\n" );
document.write( "Graph: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-x%5E2%2B3x ALIGN=MIDDLE  ALT=\"y+=+-x%5E2%2B3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C-x%5E2%2B3x%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C5%2C-5%2C5%2C-x%5E2%2B3x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );